I'm not understanding either. You say you're in debt, but you also say all your balances are zero??
Taking into consideration the student and 0 balances I'm guessing that you're PIF each month except for the student loans? If your objective is to keep things growing and boosting your scores then you're on target to do just that. The student loans will eventually start wanting payments after you graduate and if you don't go back to school for more courses. IF there's something we're missing in the original post then feel free to add to it 
OHHHHHH.... upon second read this makes more sense.... the 0% is the intro rate on balances on some of your cards? Depending on when the intro 0% expires is what you need to figure out what to pay down to not get hit with the regular APR. Good news is the interest isn't retroactive on the cards that aren't store based. If you have an intro rate on a store card you need to make those priority one to pay off to avoid the retro interest being charged since the purchase. As to the others depending on when things expire and what your regular rate is should help decide which ones to tackle first. The name of the game is to not have to pay to use credit or you lose the gains made in any rewards you've gotten from using the cards.
I think OP means 0% interest
You're not in bad shape, but as you indicated, it could snowball pretty fast.
Here is what I would do:
1. Budget so you don't have monthly carryover debt (spend less than you earn).
2. Plan your payoffs so that cards with promo apr expiring soonest get paid off or BT'ed the soonest.
3. Look at your income. If you're paid bi-weekly, some months have 3 paychecks. That is a great time to store that money or apply it to credit cards. I recommend applying if you're not good at saving.
4. Make more money. Obviously, right? But if you have a regular 9-5 job, there are tons of opportunities to grow additional income and not just MLM crap. I have three businesses that provide me random and steady income throughout the year. Really handy for debt payoff, but it can also add debt if you're business requires capital to operate.
5. Avoid most loans, especially car loans. Looking at my past, car loans were the stupidest things I ever did, not just because of interest but because new cars are expensive and depreciate fast. Mortgages are fine as long as you locked in a good rate and not buying during a bubble.
Some other tips:
1. CC interest rates are the worst, don't let those promo apr's expire with a balance.
2. Balance transfers are fine, but my rule is to never BT a balance more than once. That's just my own rule, I just don't like the idea of avoiding paying my liabilities.
3. Make sure you got auto pay enabled. That feature saves my ass.
