A couple of tips on removing screws that are badly stuck in holes.
1. Ordinary screws.
Heat the screwdriver blade first and then hold it on the screw for a few seconds - try 5 seconds to start with. The heat will transfer to the screw and weaken any glue adhesion. Try alternately loosening and slightly tightening the screw - it will eventually loosen. If the screw is into plastic, do it fairly quickly to avoid damaging the plastic. If the screw is into metal, try a hot screwdriver first. If that doesn't work, then let it all cool down and try again cold. Consider cooling faster with a little lump of ice from the refrigerator. Alternating the hot/cold treatment will almost always 'get you out of the hole'.
2. Allen keys/hex screws/bolts etc.
First, try the above heat treatment on the allen wrench or whatever tool you are using.
Unfortunately these tools are often quite small and light by comparison with a screwdriver and therefore don't retain as much heat, so might not be as effective.
If it fails, the alternative is to use, instead, a flat blade screwdriver that is a TIGHT fit in the socket of the hex screw/bolt. If you don't have a flat blade that is an exact fit, then you can carefully file a larger one to fit exactly.
WARNING: If the fit is not good and tight, you definitely risk damaging the socket of the hex screw, so take care and only use this as a last resort, but it's a very EFFECTIVE last resort and I often use a filed blade instead of the exact tool.
3. Some people hold a fine tip soldering iron on the head of the recalcitrant screw for 2-3 seconds and this is usually VERY effective, but you do run the risk of over-melting plastic, if that is what the screw is embedded in. I prefer the previous methods first and the soldering iron only if all else fails.