I've heard some sources say that the SS was one of the most diverse war forces in history and that soldiers came from over 20 different countries to fight

Its a bold statement to make, not sure if its true in an absolute sense, but it was definitely a force made up of a wide array of ethnicities.

(maybe because they had to?).

Bingo. Many units were made up of press-ganged persons; or were incorporated from Wehrmacht formations late war. A few examples; the French brigade was folded into the SS and formed the nucleus of the Charlemagne division. The "Handschar" SS from Yugoslavia was made up primarily of Croatian Muslims; few of the volunteers they had realized they were joining the SS and that, coupled with an unfavorable relocation for training caused a mutiny. This isn't unique to the SS, as the Wehrmacht made substantial use of Ost units, most notably the Georgian combat units that fought in Normandy, but in terms of percentage makeup, the SS had far more foreign troops in its service than their Heer counterpart.

I've also heard stuff like how black soldiers weren't segregated into their own units like in the american army.

This is far from uncommon; in WWI the French took command of US segregated units, Free French forces not directly under American command were nonsegregated, and so on. Segregation occurred primarily in the United States military and in the Commonwealth (to prevent an uproar from South Africa possessions).

How true are these statements and are there any resources on the subject?

This post goes into heavy detail of the multi-national makeup of the SS, how willing (or rather, unwilling) the majority of the combatants were, its effect on SS combat ability, and is sourced. I'm willing of course, to follow up on it if you have further questions.

Somewhere between 300,000 and 500,000 non-Germans were in the W.SS at one point or another; many (perhaps most) of them were conscripted, though quite a few volunteered, especially western and northern European fascists. Almost all of these men were Europeans or central Asians. The biggest sources of manpower were France, Belgium, Holland, the Scandinavian countries, the Balkan and Baltic countries (Hungary, Albania, Latvia, etc), and the Soviet Union. There were 2,500 Indians in a special propaganda unit, but they saw almost no action. As far as I'm aware, there were no African soldiers in the W.SS. Even if there had been, they would not have been intermixed with regular units, but segregated by nationality just like the other foreigners, and they would have had German officers and NCOs placed over them.

I would add that, with the exception of a very few superb units (5. SS Wiking), the foreign units tended to range from mediocre to downright terrible. The divisions formed from Russian "volunteers" were particularly unreliable.

In any case, the presence of foreign troops within an organization founded from the ground up on a basis of racism and bigotry should not be taken for more than it was. Germany was in a two-front war, soon to be three, and needed every man she could scrape up. Add to that disputes between the W.SS and the army. By controlling the bulk of foreign troops, it A) gave the Waffen SS additional power and prestige, and B) allowed Himmler to slight the army, something the SS did whenever possible.