Some of the solvents you can get into to dissolve epoxides are pretty nasty... Dichloromethane is an excellent solvent (although I'm not sure it will dissolve epoxides, and will likely dissolve the varnish on resistors and other components) but it is quite carcinogenic and toxic. Also, it's highly volatile, which means you either need to work with it in a laboratory fume hood, or assuming you don't have one of those, outside.
Dimethylformamide or aniline may work better but I have no idea where you'd get it, either in the US or abroad. They are both toxic and hazardous, read the MSDS (Material safety data sheets) online before you purchase or attempt to use them.
Epoxides are so hard and durable because they are highly cross-linked. They have an extremely high molecular weight and they are bulky molecules because of the degree of cross-linking that goes on. (you know, "bridges" that form between adjacent long strands of carbon molecules!) The problem in dissolving them is that you need to use a good quantity of solvent and you may need to do a fair amount of careful physical work as well. Bulky molecules have a huge surface area, which means that the solvent has to do a lot more work to pull it into solution. (and a lot of solvents may not have the energy to put forth!)
There are two ways to attack the problem though: If you have nerves of steel, you can obtain some nitric or sulfuric acid (doesn't have to be fuming - and WARNING!! THESE ARE VERY DANGEROUS!) and carefully break down the epoxy by applying them drop by drop. Keep some water on hand to flush the acid off the surface in case you hit something, and again, definitely do that outside.
The acid thing of course has a downside which is that you can dissolve the components quite readily, and your fingers/clothes/house/floor too. So if you do work with any of these chemicals, PLEASE do it outside, wear latex gloves, and have a large bucket of water handy so if you spill any on yourself you can flush the area before you get severely burned.
