I think paying off one loan at a time, so long as the other loans are not in default or delinquent, is an excellent strategy. If you had not consolidated all of your student loans, represented by separate promissory notes and terms, then you should be able to call the lender and ask for the pay-off on loan #xyz, for example. If you had consolidated your loans into one loan, then I doubt you can do this. Assuming no consolidation, the lender or servicer should oblige and I believe federal law provides that there would not be any early payoff penalties.

The NSLD (National Student Loan DAtabase) is really your starting point. The NSLD should have a pretty good estimate of what the payoff is and the account # for each individual loan. Make sure you receive the original promissory loan stamped paid in full after payment and that this loan is then updated on the NSLD. It may take a few months, but that way you won't have to worry about any mix-ups and you can check that the new monthly payment reflects the pay-off. If you have a problem with the servicer, you may want to discuss this with the Department of Education, FSA.