They cannot. Their half-blood racial trait means that they count as both for the effects of special abilities, spells, feats, or whatever, but doesn't necesarily make them qualify. The developers have also stated the intent was race-specific: so half-elves can't take human or elf only feats, and the same goes for half orcs and human/orc only feats.

That's why ARG had a few feats where the requirement said "Half-orc or Orc."

Quote Originally Posted by Fenryr View Post
According to this: Half-elves are Humanoid creatures with both the human and the elf subtypes.

Same applies to Half-Orcs: Half-orcs are Humanoid creatures with both the human and orc subtypes.

Same goes for archetypes and prestige classes.
Subtype doesn't mean you qualify. Drow have the elf subtype but cannot take elf only feats, for example. When a race is listed as a prerequisite, it means you must be that race - not have that subtype.