In my opinion inherent abilities should be specific things only a given race can do and that no other skill/spell can duplicate. I'll try to offer things that fit and are along the lines of minotuars' gore (unique skills). Btw, all of these are manual (require a command) and I've tried to give some durations etc...

Storm giant
Summon tempest: Here the storm giant can summon a spot of inclement weather. Aboveground, this would make weather that is, roughly speaking, optimal for calling lighting with strong winds. Underwater, one can imagine some faint whirlpool or cauldron occurring on the spot. The effects would be to increase the morale of the storm giant as well as making him harder to hit; a minor improvement to save vs spell OR denying any dust based attack could also fit. The duration is tied to how far removed the summoned tempest is from the actual weather as well as percentage and level of the giant. Must be done outdoors and a civilized area would make for a weaker tempest as well. Should be doable in combat only, like warcry. This should be a once a day (24 ticks) thing but the tempest should stick around for a bit as well, roughly like warcry again.

Cloud giant
Re-insulation: The cloud giant can focus on his affinity for cold and can heal himself in cold environments. The healing should encompass movement as well and be, magnitude-wise, around the cure serious of recent past and have a timer or perhaps 4-5 hours or so.

Fire giant
Render: Here the fire giants uses his brute strength to destroy an item. The item can be in the giants inventory, on the ground, or a door. The odds are breaking a door would need to be coordinated with picking locks but I would think that the cabinet in Tarus' office and similar containers should be openable by force with this ability.

OR

Intimidate: Using the stature and rather mean demeanor the fire giant can positively affect the moral of his group (for evils) and negatively impact the moral of his opponents (if good). This skill should allow more utility from mercenaries as well.

Arial
Shriek: Drawing on their avian heritage an arial can let out a very high-pitched cry that is somewhat painful for most humanoid races. The call will distract any foes in a room, i.e, randomly decrease chance of successful action, cause foe to attack the arial, or lower morale in foe). 2 rd lag, morale effect is not stackable and foes get more resistant to it if "cast" successively (kind of i.e. the recent sleep tweak).

OR

Perch: The arial finds a spot to land. This can only be done in suitable terrain (somewhere where trees exist but where there is some wind shelter). Perching increase regeneration rates slightly --nothing like slow or camp. Perhaps normal sleep x 1.1. Perhaps allow the arial to perch quicker than sleep from "adrenalin gushing" status.


Elf
Ward of translucence: Using nimbleness of mind and body as well as the natural affinity for magick, a high elf can appear to bend through time. The effect of this bending is subtle. The elf requires less time and mental energies in doing anything, esp. things that require/drain mana. Similarly, an elf affected by this ward takes on a greenish aura that makes it impossible for the elf to hide by any means. This should require lag (3 rds), mana, and mvs to initiate. I think once a day (24 ticks) and that it should last maybe 4-5 ticks. I see this as some ancient knowledge of the race with an elaborate ritualistic invocation to start. Its prime use is if the elf will be doing a lot of mana-based or laggy activities. It should also be useful in defending against things that subtract mana (e.g.: plague).

Felar
Sharpen: The fela sharpens his claws as a typical house cat. This can be done as often as the cat would like (not in combat and causes hide/camo/invis to drop) but has some lag. The effect is to add a slight +dam to claw attacks. This would depends on level and be of short duration. The duration could either be in ticks or actual attacks (next 10 claw attack for example).


Wood-elf
Sixth sense: In a wilderness area the wood-elf can sense invisible creatures. This skill would require some non-trivial lag (3 rds) and would function, in effect, as a form of detect invis but only in the area where the wood-elf is. If he leaves to another area then that area only can be "seen". If he leaves to a non-wilderness area then the ability drops. Another aspect so be sneaking in the woods. I can imagine some echo that the wood-elf hears creatures sneaking or maybe even creeping in the woods. The wood-elf would still need to look to figure out who snuck, crept in. This would be limited to a room, not the area. The idea is to make it difficult to surprise (via stealth or invisibility) a wood-elf in his natural environment.

Orc
Vomit: The orc's rather vile diet, compared to other humanoids, results in a particularly nasty gastric juice. The orc can vomit some of this substance and use it to coat a weapon. The effect of being hit with such a weapon would be a form of nausea that would cause a slight lowering of con, dex, or str (determined randomly). The orc should be able to do this only immediately after filling his stomach (eating as much as possible as opposed to just topping off).

For humans, dwarves, half-breeds, and underdark races I'm drawing a blank currently...