Wits would be more like intelligence and cunning and nerve more like willpower. How I imagine it: there would be turns and rounds. At the beginning of the turn each player throws as many dice as he has nerve. So lets say it's three and you throw 1,2,6. The second player has four nerve and he throws out: 2,2,3,4. The turn has six rounds. In the 1st round the first player attacks, in the second both (the one with higher agility first), in the 3rd round the second player, in the 4th the second one, in the 5th none and in the sixth the first one.
And many of the things you wrote would be just determined by skills and not attributes. So this is how I see it now:
Strength - amount of life
Agility - who attaks first
Wits - amount of skills? this I'd rather change
Nerve - amount of rounds
Strength - sounds good, would this also determinate your physical attacks?
Agility - Agility would be better if it was renamed as "Reflexes".
Wits - Amount of skill points during character creation, or in total?
Nerve - So if I understood it correctly. Nerve attribute is your "Action points". I would make action points standard, because currently it is the attribute you need to have maxed out in order to be a badass.