Heh, the problem with racial discussions is that so many terms are tied into systematic oppression of groups who really did have terrible things done to them.
In the US, the most polite term for a person of majority sub-Saharan African descent is "African-American;" "black" is also considered okay. "Mixed race" sometimes comes up.
"Negro" is a dated term and while still used by a few organizations which have long histories, is generally used by older folks who don't care to be polite about their racial discussions. Anything "-oid" has connotations associated with the old Eugenicist movements back in the 20s and 30s and should be avoided.
It's complicated, but being polite in times of weirdness is something that can be complicated. In general, you should be fine with "black." There are a decent number of folks who would seek to correct you to "African-American," if you're speaking of the descendants of American slaves and more recent immigrants who resemble them. The polite response is to acknowledge the correction and speak in the term they prefer.
The general term for a person who is Hispanic, Asian, or African-American is "persons of color," which is a bit of a mouthful but works fine.