Unfortunately, there is no detergent that you can use to eliminate the damage caused by years of lax maintenance. And, once you see trans fluid that is dark and burnt-smelling, the chances of getting many more miles out of that trans are...not good.
However, I would recommend changing the fluid, and I would recommend that you go to an independent trans shop (NOT AAMCO, Lee Myles, Cottman, Mr. Transmission, or any other chain) for this service. If you are a particularly lucky person, the fluid change may allow you to get a bit more life out of that trans.
As to the PS fluid, I'm not quite sure how that would have gotten burnt also, but I guess that anything is possible. If you saw it and it was foul-smelling, then--yes--it should also be changed.
Just for future reference, trans fluid should be changed every 3 years or 30k miles (whichever comes first), even if the mfr does not list this procedure in its maintenance schedule. There is a trend toward car mfrs using "lifetime fluid", but that terminology is essentially meaningless IMHO, and the fluid would still need to be changed on the above-noted schedule.
Many people never change their PS fluid. I do it every 60k miles, but I do tend to be a bit obsessive with maintenance.