Is there a way to sharpen/restore old files?
Yes. The classic old method to sharpen a file is vinegar sharpening which is exactly what the name suggests, soaking the files in vinegar.
Now that we know the active ingredient in vinegar is acetic acid we can make the obvious educated guess that it's an etching effect from an acid. And it is known that other acids do the same job and were used in the past. Two of the best alternatives because of easy access are citric acid and sulphuric acid (e.g. battery acid). It's best not to use hydrochloric even if you already have some, many sources speak of the risk of hydrogen embrittlement when using HCl so it's best not to risk it since files are already brittle enough.
Acid etching works best on files where they are not heavily worn but are just rounded from use and no longer cutting well. Where there is any scoring/scratches or the teeth are worn down so far that there are flat shiny patches (hard to believe but you do occasionally see old files that had been used that hard!) you won't recover a usable surface. But files are nearly always double-sided and because this is inexpensive and largely a hands-off process that mostly requires patient waiting it can be worth it for a file even if it only has one side worth salvaging.
You say you've used solvents and that is one good way to start the process off as a file must be thoroughly degreased before soaking in acid to give it unimpeded access to the metal, ensuring even results.
In addition to organic solvents you can also soak in oven cleaner, or a hot solution of washing soda. Both will eat any form of grease and pose no harm to the steel.
If you want to use solvents I wouldn't rely on mineral spirits/white spirit alone, soak in spirits to begin with then dry off and brush down or soak in acetone or lacquer thinner.
If the files have any clogging this should be removed before etching, again to give the acid full access to the surface of the file.
In addition to using a 'file card' (a type of brass-wire brush specifically intended for cleaning swarf from files) there are other methods, including pushing in the direction of the grooves using the corner of a scrap of hardwood or the edge of a piece of brass. But some material clogging files can be very tenacious (a good example is aluminium) so you will sometimes have to resort to picking bits out of the teeth patiently with a needle or another sharp steel tool. If using a needle your hand muscles will thank you for chucking it up in a pin vice or permanently mounting it in a wooden handle rather than just gripping the needle in your fingers.
This picking away is just as tedious as it sounds, and can take anywhere from a few minutes to an hour of concentrated work per side, but it's worth every second of the effort.
You may want to quickly degrease a file again after cleaning, especially if you've done the work with bare hands.
Note: you can clean first prior to the degreasing step, but I've found that clogging residue (esp. wood) can be much easier to remove from a file that was thoroughly degreased first, and it's easier to see it all anyway.
As you might expect if the file is rusted soaking in acid will simultaneously clean the rust from it, so this is a very useful technique for secondhand files picked up from various sources since you'll clean them of rust while also improving how they cut. But don't expect too much if the file has any heavy rust encrustations, after the rust is gone some pits can be left behind. While on some tools pits can be merely a cosmetic issue on files they can impact performance, in the worse cases leading to irregular abrading of the workpiece or scratches.
After soaking in vinegar or another acid even after rinsing thoroughly the files may start to rust again very quickly (flash rusting) so it's advisable to give them a quick spray of something like WD-40 immediately after to help halt this process.
So here are the steps:
- brush off any loose matter
- clean off all debris
- degrease a second time if thought necessary
- soak in your chosen acid*
- rinse thoroughly then give the file a quick scrub with a stiff brush (a toothbrush is ideal) using common hand soap
- pat dry
- shoot with WD-40 or another water-displacement agent, or dry thoroughly using a hairdryer or by placing in a warm oven
*No real guidance can be give on the time needed to soak a file. Using vinegar for example while you can typically get some improvement with just an overnight soak, with some vinegars, on some files, you may need to soak for two or more days before you judge it has done all it can.
The strength and concentration of the acid being used, the coarseness of the file and the amount of wear all have a huge impact on the time needed. So for stronger acids on finer files you may want to remove them from soaking after just an hour to check progress, with a weaker vinegar on a coarse file leave overnight to begin with and expect that it might take much longer to achieve the desired result.
When the process is completed the file should be quite uniformly dull and grey, and rubbing a thumb over the teeth it should feel very 'grabby', much more so than many files are straight from the factory.
Here are some self-explanatory pictures of the restoration of some files I bought last year:
And here they are with the work completed, with handles:
Note the characteristic dull grey appearance of files treated this way.
There are commercial file-sharpening operations out there in the world and some people rave about the quality of the work. Some users are so impressed by the results — often stating that files treated this way are sharper than any you get straight from the factory, irrespective of cost — that they buy new files and send them straight to be sharpened before ever being used.
It seems fairly certain that these companies don't do any sort of re-cutting of the file teeth as one might first think, but instead they all use some form of acid etching. Although they may have any number of additional steps (including post-etching treatments to improve rust-resistance) there's no reason to suppose you can't get results similar to or as good etching your files at home in the manner described.