|Sources explaining relevance to gentiles:
- Rambam, Mishneh Torah, Maaseh HaKorbanos 3:2
Gentiles may only bring olos to the Temple, not sin-offerings (apparently same for bamos elsewhere; thus no minchah sin-offering, either).
- Rambam, Mishneh Torah, Maaseh HaKorbanos 19:16
Gentiles may offer olah sacrifices on bamos in any location (implying not chataos, ashamos, shlamim, or menachos).
- Rashi, Talmud Bavli, Zevachim 45a (Akum la maisu
Gentiles may only bring nedarim and nedavos, thus only personal olos and shlamim, not sin- or guilt-offerings or maasar behemah.
- Rambam, Mishneh Torah, Melachim 10:1
Other than for manslaughter, gentiles are not liable for sinning as a shogeig.