Ok, this is a huge question since you are asking about a lot of people and how they were impacted. Also, I am not really sure what you mean by how it culturally impacted them so please ask for clarification/more info should my response not answer the question you had in mind. I will try to answer this for all groups you mentioned but it is easier for some than for others, so please forgive me if I won't be able to cover all of them.

Generally, it can be said that for all of these groups or parts of these groups (e.g. the cultural impact for Black People in Germany was a different one than for those in, say, the US. And Slavic people are not really one coherent group except in the the Nazi definition) the Holocaust has made a cultural impact in that the narrative of having been a victim of Nazi persecution has become a part of their national/political/religious/group identity in various and often empowering ways.

For example, in the late 70s with the gay rights movement on the rise (male homosexuality had remained illegal in Germany after the war and the persecution of many men who had been imprisoned in the camps had continued) and following the first inquiries into the persecution of gay men by the Nazis through films and memoir literature, thepink triangle used by the Nazis to identify gay prisoners in Concentration Camps became used as a symbol for gay rights. Signifying their history of persecution, the symbol and the history behind it was reappropriate by the movement in order to highlight the injustice of their continued victimization and persecution in Western societies. The usage of this symbol as a signifier for the unjust treatment of gay men and homosexuals in general, took off especially with the HIV/AIDS epidemic in the 1980s. It served, according to the glgbt encyclopedia as "as a reminder of past and current oppression and a tribute both to those who died in the camps and to those who were dying of the new disease." Subsequently, the symbol has also been used by several anti-AIDS coalitons as well as several monuments commemorating either specifically the homosexual victims of the Holocaust, e.g. in Dachau or Vienna or more generally the victims of anti-gay persecution and violence, e.g. in San Francisco. While the use of the symbol has not been entirely uncontroversially, it is an example of a group of victims of the Holocaust not only reappropriating the symbols of their persecution but also integrating Nazi persecution into an identity and political narrative designed on the one hand to project the injustices they suffered to outsiders on the other hand highlighting the trials overcome by the community to the inside.

A similar phenomenon can be observed with Jehovah's Witnesses. I'm far from an expert on this group -- since there is hardly any non-Witness literature on the subject, it seems I am not the only one in that -- but especially in a community whose members could have through a renunciation of their faith been freed from the camps, the willingness of many of the persecuted to suffer horrendously and die for their principles has been integrated into an identity narrative to be projected on the out- and inside. In short, the Nazi persecution has given this religious movement examples of their faith to be praised. For further information, I would recommend reading Detlev Garbe's book on the subject of persecution and maybe perusing some of the watchtower archives since if I recall correctly stories from the camps are featured there frequently (at least in the German edition).

As for Poles, Soviets, French, Yugoslavians etc. the persecution of their countrymen and -women because of racial and political reasons has found their way in virtually every national identity narrative in formerly occupied Europe. Generally, we can distinguish here between Western societies, which like Franc and the Netherlands have developed narratives of resistance that have only been challenged from the late 60s onwards but really broken open by the 80s when conflicting narratives about resistance and collaboration have become more frequent. Then there are the formerly socialist countries, where for obvious reasons as long as the regime lasted a narrative of the Nazi persecution being part of the international class struggle between communism and capitalism has been heavily pushed (the Soviet Union with the double memory of the patriotic war and the socialist war; Poland with a very strong nationalized narrative; and Yugoslavia are the exceptions here though I painted this with a very broad brush); and the successor state narratives with West Germany being torn between responsibility and victimhood, Austria embracing victimhood a la France and East Germany embracing the socialist model, all with their own narrative however.

Probably the most interesting case here are Yugoslavia (though since it is my area of expertise, I am slightly biased here) and Poland. Yugoslavia's national narrative from 45 to the 1980s was pretty much dominated by the Partisan version of the past. From the unique model of Yugoslav socialism to the concept of brotherhood and unity, a lot went back to the fight of national liberation against the German occupiers. In this sense it is not surprising that with the start of national tensions in Yugoslavia, a main point of contention became the history of WWII, especially re: Serbian victims of the Croat Ustasa.

As for Poland, even under socialism there had always been a national narrative of Nazi victim hood rather than a purely socialist one. This stems partly from the historical experiences of Poland pre-WWII, partly because of the strong national narrative of being divided between Germans and Russians before. There especially, Poles as victims of the Nazis (and in recent years also of the Soviets) have become a very strong and central point in the official version of national identity narrative. One only needs to look at the various controversies of recent years during which Poland and its citizens have strongly objected to the moniker "Polish concentration camp" for Auschwitzn or at the exhibition in the Auschwitz memorial in the former Stammlager, which speaks of Auschwitz as a heavily Polish rather than Jewish experience (which to a certain degree at least when it comes to the Stammlager, it also was).

As for Roma and Sinti and other groups persecuted by the Nazis as so-called "gypsies", there too -- similar to but in a certain sense even more than gay rights activism -- the Holocaust respectively the systematic murder of their own, the Porajmos was a huge cultural and identity issue, especially in the fight to be recognized as victims, which in Germany didn't happen until 1982. Some of the trends in the community re: commemoration and cultural impact are really hard to pin down though since there is a tradition of oral remembrance among certain groups and the production of written testaments that could give a glimpse into Romani commemorative culture in the post-war years was also severely hampered by their continued persecution and poverty. But rest assured, it did have a huge cultural impact at least in some communities such as the German one.

Edited to add Addendum:

Unfortunately my knowledge of Afro-German culture and the research done into their history outside of the Third Reich, their identity, and commemorative practices is very limited but I wanted to add this:

Outside attention as well as identity politics for Afrio-Germans really only took off in the 80s after May Ayim and Katharina Oguntoye wrote their book Farbe bekennen about the experiences of Black women in Germany. After years of community work the Association of Black People in Germany put together an exhibition called "Homestory Deutschland" featuring 27 biogrpahies of Black people throughout German history including people suffering from Nazi persecution. They write that this exhibition is to be understood as a "collective biography" of Black life in Germany.

Sources:

As I said, this is a huge question and if you want more information and/or sources about particular groups, please ask because here I will try to give you some sources that give an overview over memorializaiton and cultural impact of the Holocaust in general.

• Daniel Levy and Natan Sznaider: The Holocaust and Memory in the Global Age.

• Alan S. Rosenbaum. Is the Holocaust Unique? perspectives on comparative genocide.

• Barbara Engelking, ‎Gunnar S. Paulsson, ‎Gunnar Paulsson: Holocaust and Memory.

• Amos Goldberg, Haim Hazan: Marking Evil: Holocaust Memory in the Global Age.

To add to what /u/commiespaceinvader has already said, it can also be noted that the Holocaust has been utilized by all of its victim groups in a few different ways (I recognize that I will be generalizing, but such is a necessity).

Typically, victimization has been used (please do not read a negative attribution to the usage here) to: form communal identity, gain acceptance or other benefits, and absolve guilt/redirect blame.

As to the first, I believe that /u/commiespaceinvader has sufficiently demonstrated how this is the case. Various nationalities and cultural groups have identified themselves as victims in order to form identities. His example of the use of the pink triangle is a premier example.

Second, groups which receive cultural acceptance as victims gain benefits of that status. While it may seem untoward to speak of benefits of victim status, we are not speaking of individuals, we are speaking of group identification. Remember that one not need be a victim to be a recipient of group victim status. For example, in my studies (US representations of the Holocaust), there is a clear increase in cultural and academic works on the plight of gay men in the Holocaust that corresponds with the Gay Pride movement. The first Gay Pride parade (1970) took place roughly a decade before the first academic work on the persecution of gays in Germany between 1933 and 1945. Similarly, Bent a groundbreaking play about this persecution, opened in 1979. Such cultural and academic works buoyed the movement by allowing associating opponents of the movement as similar to the Nazis. Other groups have gained such benefits as financial restitution.

Finally, there is also the absolution guilt/redirect blame. One of the clearest examples of this, in my studies, has been the case of clergy victims of the persecutions in Nazi Germany. Textbooks written in the 1940s and 1950s continually note clergy as victims of the Nazis in the same locations (and sometimes with almost as much textual coverage) as they discuss the Jews as victims. As such, clergy and Jews were depicted as being persecuted for religious reasons (inaccurate in both cases) and as having similar experiences. The reason for clergy being depicted in such a way seems to be a way in which a culture (U.S.) built on similar Christian principals to that of Germany could depict Christians as having been victims of the Nazis instead of, at best, bystanders. /u/commiespaceinvader already noted that a number of national groups used their own victimization by (Poles) or resistance to (French) the Nazis to deflect from the participation of many of their members in the extermination of the Jews.

Indeed, the appropriation of the term Holocaust by so many groups has created the situation in which it is difficult to speak of the Holocaust and truly understand what one means. This is, in large part, what gives such power to the term.