I took it to mean the profits were around the amount of the debts (around 50k on 52k debt), but their savings (whatever that includes, 401ks or whatever, but definitely including the home sale profits) are around 125k, so using the 50k home profits would reduce that savings amount by 40%.
In any case, that aside, I personally would pay the minimum amounts on all of those loans (as long as the rates are fixed for the life of the loans) all the way until they eventually pay off years from now, and invest the house profits.
Of course, it depends on how much the debt bugs you, but the mathematically correct answer* is to invest it. The emotional choice could go either way, depending on your feelings. Some can't stand debt. I can't stand leaving money on the table.
*Defined as you would have ended up with more money most of the time historically had you made that choice - it's more likely with you to end up with more money, though not guaranteed.