Here would be one type of D&D response. The one red eye for the Wizard could be a magic eye; ie a glass eye that through magic enables the wizard to cast more spells, or see invisible objects, or whatever powers one can think of within reason.
The Orcs have red eyes because they are able to see in the dark, an ability called "infravision." One of the side effects of living underground and their more "animal" make up. It's like viewing objects in the infra-red wavelengths kind of like "night vision" lenses the military uses.
Dwarves have infravision but because dwarves are more "human-like" their eyes aren't red.
Like Doodstormer said, the red eyes of the skeleton's could be due to the type of magic used in their creation.
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