Well, I'd definatley give penalties for doing anything requiring coordination, penalties depending on level of drunkeness...I suppose one could even make a 'Drunkometer'...

Buzzed: No Change
Tipsy: -1 to certain skills
Drunk: -2 to certain skills, and maybe initative
Wasted: -3 to certain skills, initative and some can't even be used
Obliterated: You're useless and staggering, halve all dice pools for skills that can even be used(id allow combat skills but not much else.)
Of course, you could do a -2/4/6 if you are feeling up to it.
Or you can just work the stun damage monitor, which might be a lot easier. Fill the monitor, pass out.

Perhaps you can use the above meter to gauge how you behave if you have to function with a hangover...
However, i'd also grant Pain Tolerance equal to the dice pool penalty. I can vouch for this one personally....I had a rather injured knee one night after a friends celebration of something or other at a bar...and i didn't even realize it til the next day. Oops.
If you really want to get technical, you can even make a chart determining how many drinks it takes. I assume for a decent rule of thumb is about 1 drink an hour per 50 kilos of weight keeps you safe...anything more requires a body roll, and start making a threshold for each drink after that, raising the bar each one.
So, a human with Body 4 who weighs about 80 kilo id say can pound a drink an hour safetly...if they do 2, make em make a body test(1 hit necessary). 3, Body test, threshold 2. And so on. a 200 kilo troll should be able to handle a lot more of this. Of course, Resistance to Toxins adds to this body roll(it IS a toxin, after all.)
Of course, if they have cyberlimbs...make it easier for them to get drunk. Less blood in the body-less booze you need to intoxicate it.
For humor purposes, perhaps grant Irish, Finnish, Germans or Russians a +2 to their dice pools

(joking, guys.)
And i find it sad the first mechanical thing i could contribute to this game is a Drunkometer. Well, i do work in a bar...