Ok. Let's see if this makes financial sense:
FHA let's you cash out equity up to 85% of the value, however, that means paying mortgage insurance. With $74,000 available to pay the existing mortgage ($4000 in closing costs), you'll have just enough to cover the loans. Mortgage insurance is not tax deductible. Student Loans are. So, not so smart idea to go that way.
Conventional lending goes to 75% of the value, giving you about $10,000 after paying $3000 in closing costs and fees. However, in going that high, your rate is affected because of the points associated with pulling equity to 75%. The best figure is 60% max, however, that won't cut it. At 70%, you'll have about $6000 to play with (after paying $3000 in closing costs).
Now, here is where having more information about you helps. Of course, don't go public with this, but how much have you saved for retirement so far? Do you have or expect to have children one day? If you have retirement set up, where is it?
What I'm getting at is that if you are going to use equity to pay off debt, then you'd better already have your retirement plan set up. Do you want to reach retirement age and say,"Look at me! I'm debt free but I'll have to work till I drop dead"? Or do you want to be able to say, "Look at me! I can retire young enough to enjoy life and use my retirement money to pay off my debt"?
The biggest problem people make is they focus more on paying their debtors, rather than paying themselves first. We put so much emphasis on our credit report and our debtors and we forget about making sure we can live comfortably. You have to pay yourself first.
Where to save? Check out youtube.com and search: Doug Andrew IUL. This life insurance product will make you think twice about your IRA's, 401k's, Roth and social security. Here's a few simple questions to think about: When you retire, what will be your income tax bracket? If you don't know, why are you investing your money in a product that taxes you when you retire? If you think that the $500,000 retirement balance is yours when that time comes, think again. If your tax rate is at 70% (like it was in the 1970's), you're only going to live on $150,000. Aha, the Roth IRA doesn't require you to pay taxes because you pay post tax dollars into it. However, you are limited to the amount of money you can invest per year and the amount of IRA's that can be open annually. You can open as many IUL's as you'd like.
So, to answer your question, yes you can refinance and pay off your student loans. Does it makes sense? No, but that's just my opinion.