I'll give a contrary view to what may end up being the consensus.
Assuming: 1) job lined up post-grad (or essentially a lock); and 2) big pay increase as of that time, I'd probably not worry too much about paying the debts down yet. Do try to figure out where the money is going. Charge/debit everything (and pay off at statement or sooner if charge), or keep a small notepad to enter all cash payments. If, after doing that for a month or so, you find that $$ are being wasted, then address it. I suspect that some/most of the leakage is legitimate.
If you have to move, buy professional clothing, or anything of that nature in connection with new job (or have to job hunt), you'll want as much cash as you can gather on hand at or before the end of the year. Thus, even if you find expenses to cut, it may make sense to add to the emergency fund rather than throwing it at what appear to be relatively small loans.