I’m looking for at races for a Rage Prophet, Barbarian/Oracle prestige hybrid class, and Was mostly going by the stat bonuses the races give me but I noticed Half-Orcs get class bonuses to both Barbarian and Oracle. I feel like I already know the answer but wanted to ask if anyone could confirm whether I would get both classes bonuses.
I don't see anything that indicates half-orcs get two favored classes. In pathfinder everyone gets 1 favored class. You can pick whatever you want as your favored class it just can't be a prestige class. Once you've picked your favored class every time you gain a level in the class you picked as your favored class you can either get 1 extra hitpoint or 1 extra skill point. Some races will give you a third option with certain classes. For example, if you are a half-orc and have chosen barbarian as your favored class you have the option of gaining 1 additional round of rage. So, as a half-orc barbarian you could either get 1 hitpoint or 1 skill point or 1 extra round of rage per day.
Taking levels in a class that is not your favored class yields no bonus. Not every race gives an extra option for every class in which case you only get the choice between an extra hitpoint or an extra skill point.
Half-elves get a literal multi-class bonus in the form of the racial trait Multitalented. This allows a half-elf to pick two favored classes instead of one. So, if a half-elf picked barbarian and oracle as their two favored classes then any time they gain a level in one of those two classes they can choose between skill point, hitpoint or any other options available as a half-elf.
Pathfinder changed things from 3.5 so that instead of being penalized for multi-classing, you get rewarded for not multi-classing.