I’ll preface this by saying that I can’t speak too much about the Armenian settlement in California, though I can say that it dates back to the early 1900s, and did grow in the 1920s as refugees from the 1915 genocide arrived: in particular, Andranik Ozanian and Soghomon Tehlirian both moved there; Andranik was a major leader in the Armenian independence movement during the early 20th century and a leading military figure; Tehlirian is famous for assassinating Talat Pasha, one of the Ottoman leaders who instigated the 1915 genocide; I will admit I just found out they both moved to California at this time, and credit to /u/Lyovacaine for pointing that out.
To give some background on the Armenian diaspora, which I can talk to about: Armenians have historically had communities spread around the world, and are famously known to have been in places like India for centuries. They are also prominent in places like Ukraine (Lviv in western Ukraine was known for it's prominent community of Armenian merchants), and were well-known for being merchants, utilizing this diaspora for that purpose. The 1915 genocide further displaced the Armenian community, and those who survived the trek into the Syrian desert either settled there (in modern Syria and Lebanon; both have large Armenian communities today), or emigrated, with France (namely Marseilles) and the US (Los Angeles) being the prime destinations (I'll also note Montreal in Canada has a notable Armenian community, as does Mexico).
Why Armenians moved everywhere but Armenia is a relatively simple answer: the modern state of Armenia is on the eastern fringe of historic Armenia, which stretched across eastern Anatolia. At the time of the genocide, the number of ethnic Armenians in what is now Armenia was rather small (I don't have exact figures at the moment, but will be happy to find them), and Yerevan, the capital, was an insignificant village mainly populated by "Tatars" (what we who call Azerbaijanis today). The First Armenian Republic, which was established in 1918 and lasted until the Red Army invaded in 1920, was a poor country, and as the first Armenian state to exist in centuries, it did get a large number of refugees. However they were unable to properly help people, and once the Bolsheviks took power the border was closed, so many did not venture there, instead going overseas.
As for the final part of the question, about Georgians and Azerbaijanis: both of those groups have historically stayed close to their land. Georgians did spread out in the Soviet Union, and gained a reputation for business dealings (both legal and illegal; the Georgian mob was infamous for its activities), but they were never as widespread as the Armenians. Same with the Azerbaijanis, who have historically kept to their area, and with the development of the oil industry since the 1880s have had little reason to leave (the capital Baku was, and remains, a major oil city of the world).
I'm not a historian and my answer will probably be deleted but I am an Armenian from LA so maybe I can give a little answer. After the Armenian genocide a lot of Armenian heros like Andranik Ozanian and Soghomon Tehlirian moved to California to places like fresno. A lot of Armenian families followed in their footsteps. Also one must take into consideration that the US adopted tens of thousands of Armenian orphan children during the Hamidian Massacres and the Armenian genocide. Woodrow Wilson tried to create a US mandate for an independent Armenia that would encompass modern Armenia and parts of Western Turkey so many Armenians that left Armenia found America as a sympathetic second home. There is a large community of Armenians on the east coast like in New Jersey and Massachusetts. One of the reasons there are more Armenians then let's say Georgians or Azeris in US is because for decades Armenians were being slaughtered and having to fight for survival (against Azeri and Turkish ethnic groups and others) and Armenians are used to living outside of "Armenia". There have been Armenian communities in India and Singapore, Austria-hungary, Poland, Venice Jerusalem, Cilicia, Lebanon, Syria and other places all through out history so Armenians moving away from Armenia to foreign lands during hard times in the homeland is more common then let's say an Azeri or a Georgian and to the fact that Armenian culture has a lot of things that are similar to western culture and ideology and the fact that Western countries bring a stability that Armenia doesn't have because of wars and genocides at the the hands of turks and Azeris. Add on top that many Armenians had to flee the soviet union for being patriots and being participants of the Armenian fedayeen revolutionary groups which defended the Armenian communities against Turkish, Kurdish, and Azeris that would attack Armenian communities. These groups also had western ideology in it. So these groups and people were being rounded up by the Soviet Union to stamp out all nationalists that wanted a free and independent Armenia and many of these nationalist were sent to gulags but many left Armenia and moved to Western countries. Once the soviet union collapsed a lot more Armenians decided to emigrate out of the country. At the time Armenia was in a blockade and at war. We had almost no power or fuel and our only lifeline was through Iran. Over 300,000 Armenians were kicked out of Azerbajan and Many of these people were descendants of Armenians who were survivors of the Armenian genocide and instead of just moving to Armenia Many of them left to America and other Western countries. Many Armenians decided to leave the country and many moved to West coast and East coast US where there were already large Armenian communities that could help integrate them into the country.
So at the end Genocide and massacre and US adoption of orphans were one component of large Armenian community. The other is support from the US for a new large Armenian country after the end of ww1. Famous Armenian heros moving to US helped fuel more Armenians to these regions. After the Soviet collapse and 4 years of devastating war in a resource less Armenia and a blockade by Azerbajan and Turkey also helped enlarge these communities.
Sorry for any and all mistakes typing on a phone at work will provide some sources soon
While the LA/Southern California area has the largest Armenian community NOW, it has not always been that way.
The first major wave of Armenian immigrants who came during/shortly after the Hamidian Massacres and Genocide settled largely in Watertown, MA, NYC and Fresno CA area. NYC was just a major hub for immigrants obviously, and had ample job opportunities. Watertown and surrounding New England cities (Worcester, Providence RI, Hartford CT) I'm not too sure on New England exactly, don't know that many Armenians personally from there or have done research. Fresno was largely agricultural based. I think Watertown was the largest community for quite a while. There were also significant populations in Detroit, Milwaukee, Chicago areas, and many other midwestern cities (usually due to manufacturing jobs).
Regarding LA area in particular - it was never a significantly large community until the 60s and 70s. They had some Fresnoites migrate in the 20s because of poor farm yields around the depression and a few people who opened small businesses (carpet stores in particular). When Armenians from Lebanon and Iran left their old countries during the Lebanese Civil War and Iranian Revolution in the 60s and early 70s, many settled to LA. Parskahyes in particular were drawn to LA, as Libanahyes mostly moved to Detroit. This is where my knowledge gets a little fuzzy, but I think there were a few prominent and well off Parskahyes who already lived there due to people who moved to the US for higher education and decided to stay in the country because they became doctors and what not. Hollywood was the largest destination for that wave.
Glendale becoming "Little Armenia" happened more during the 80s and 90s. Like many other immigrant groups, Armenians often clustered in areas were many other co-ethnics lived. Especially for immigrants who don't know English well, being around large amounts of people of your same ethnic background can help ease the transition to their new country. When Armenians emigrated away from the Soviet Union en masse, LA was a hot destination due to the now large community or primarily Parskahyes, since they also spoke Eastern Armenian, while the genocide survivor and Lebanese communities were Western speaking. Glendale in particular was because they had affordable housing because the was heavily developed during that time. Many Soviet Armenians had basically nothing when they arrived in the US, especially after the fall of the Soviet Union.
This academic article "But Why Glendale" has even more information https://escholarship.org/uc/item/6v04w06x#main