I’m going to assume that your federal tax delinquencies are for federal income tax and that no portion of the liability is due to fraud. If that is the case, then your tax liabilities may be eligible for discharge in bankruptcy. The general rule is that the an income tax liability is eligible for discharge in bankruptcy if it has been (1) at more than 3 years since you filed the return to which that liability relates and (2) it has been more than 240 days since the tax was assessed (this second part is there for audit adjustments, etc). However, any debt, including tax liabilities, that are due to fraud are not dischargeable. So it may well be that even if the student loans are not dischargeable that the bankruptcy could help you with the tax debts and that might give you some needed debt relief.
The statute of limitation (SOL) for collection of a federal tax liability is generally 10 years from the date that the tax was assessed. There are, however, several things that toll (suspend) the running of the SOL. One of those is the filing of bankruptcy. So, if you file bankruptcy any taxes for which the SOL is still open when the petition is filed and that are not discharged in the bankruptcy will have the SOL extended for the time the IRS is precluded from collecting in the bankruptcy plus six additional months. There are other things that extend the SOL, too, inlcuding submission of an offer-in-compromise (OIC), extension by a waiver signed by the taxpayer (generally in connection with an installment agreement), and any extended period of time the taxpayer is outside the U.S.
What this means is that you want to consider carefully whether the taxes are likely to be discharged in the bankruptcy and, if not, what bankruptcy will do to the SOL for collection for any non-discharged taxes in deciding whether to file bankruptcy and how to time any petition for bankruptcy.
BooRennie has already provided you information on the student loan part of your question. It is pretty difficult to prove the undue hardship necessary to succeed in discharging student loans. I suggest you discuss this with a bankruptcy lawyer who is experienced in dealing with student loan debts in bankruptcy to a realistic view of how likely it is that you could get these debts discharged.

