*all information pertains only to federal student loans and not private loans
To OP: Yes, pay down your student loans first. Depends on the person, but the peace of mind that comes with lowering your liabilities is worth it to me to pay down the loan debt even if you had a near-guaranteed 6.8% investment vehicle. I'm just going to assume you aren't on the verge of being kicked out in the street for this next part. Don't wait until the deferment period is over to start paying the $900 or more than that. Do that now! One reason is that interest can be capitalized during this time (interest accrued during deferment can be added to the principal amount). The other is obviously the sooner you start paying, the more principal you will be able to attack. Student loan payments covering the whole 10 years (or gasp! the 25 extended) are for anti-mustachian suckers. Don't let that deferment period being over earlier than anticipated get you down. Rare caveat: if you go off the grid and can avoid most of society for 25 years, then your loans and any interest will be relieved entirely but creditors won't be as friendly and not many people I know like debt hanging over them for such a period (especially when that debt isn't at least putting a roof over your head) and it also begs the question, why did you get the loans in the first place?
I can't attest to all federal student loan lending websites (as there are several) but myedaccount.com is what I use to pay mine off and you will be able to see how much of your payments are interest and how much are principal. You will also see each separate student loan and how much of that $900 (or however much the amount is) would be going toward each one. Also, enroll in the automatic debiting program which takes the funds directly out of your bank account. This will cut off .25% from the interest rate. Another good benefit of the automatic debiting is that it automatically does this every month until you modify it in some way. This sounds silly and not like much of a benefit but here is how the standard automatic payments work (auto payments that aren't taken directly from your bank account), say 6 months from now you pay $1350 in your first 2 months. That is $900 more than the payment plan called for and equal to 1 whole payment on that specific plan. So you wouldn't owe a payment for that 3rd month according to the payment plan. Then of course, with your balance level, the next payment you did make (3rd payment in 4th month) would likely be all interest since it had been accruing for 60 days. The automatic debiting takes whatever amount you specify out of your account every month no matter how far ahead you are. You can always add one-time payments even on top of the automatic amount being debited but you typically always want to be hacking away at that principal every month.
Another suggestion if you are not doing this already: move your loan payment date to the earliest date you can of each month (I'm allowed to choose 7th, 14th, 21st, 28th). This will be a one-time major principal benefit with every payment after that marginally more principal-laden. How? Say you pay on the 21st but then move the payment up to the 7th. Depending on the month, that payment when you move to the 7th will only have 16 or 17 days of interest on it rather than the normal 30-31. So your first payment on the 7th could very well have a couple hundred extra dollars worth of principal in it relative to a normal payment of the same size (I have/had a similar amount of student loan debt and my principal increased by $240 for that one payment in which I moved the date up). Then of course, every single payment after that will be marginally better as you are working with a slightly lower principal amount compared to if you had never moved your payment date. i.e. 30 days of interest on (77k-200) is lower than 30 days of interest on 77k. I know this isn't some drastic idea but whenever you have loan balances this high, it can be comforting to zap a few hundred extra dollars off that principal even if it doesn't mean much in the grand scheme of the entire balance.
NOTE: you need to be enrolled in the automatic debiting program otherwise if you change the month of payment, your next payment date won't be due until the next month. e.g. If you make a payment January 21st and want to move it up to February 7th for the next one, you need to be enrolled in the automatic debiting program otherwise the next payment won't be made until March 7th (again, accruing all sorts of interest).
Lastly, when you look at payments, you will see how it is broken down to each individual loan. You mentioned not all of your loans are at 6.8%. You can't touch the payment plan breakdown each month but what you can modify are the extra payments. You can specify that additional one-time payments (sorry, non-automatic payments only) only be put toward the 6.8% loans while ignoring the lower interest loans. Again, these are for payments in addition to the monthly amount. This way you attack the higher interest loans more so relative to the lower interest ones.
As for the deductible loan interest, once you get to the end and you are left with hopefully your lower interest student loans, it might make sense to hold off at the end of one tax year so that you can extend the tax deduction into another tax year (at least partially if you were already over the $2500 benefit limit and were wavering on whether to finish them off completely or stretch it out into the next year). Please note this really only comes into play at the very end and assumes the bare minimum monthly payment is still being made, don't try to extend your loans just so you can deduct $2500 from your taxable income in more tax years when your additional interest you will be paying as a result more than cancels out the benefit.
To menorman: Yes, you can deduct $2500 student loan interest every year from your taxable income via the 1098-E form. Yes, you also don't have to itemize to receive the benefit either. However, this is not a tax credit, just a reduction in taxable income (a tax deduction). This is not a dollar for dollar match like a tax credit is. Thus, the realized savings or "extra income" are much less than $208/month. At the 28% bracket, it will save you $700 or $58.33 monthly. At 25% bracket, $625 or $52.08 monthly. At 15% bracket, $375 or $31.25 monthly.
