Before you try to move any screws give them a few days soak in PlusGas or similar. Depending on how badly mucky the components are with old grease, dirt etc. I give parts a good spray of WD40/GT85, let it soak in, and then use an old toothbrush and rag to clean.
Record front changers will strip down quite easily. Release the spring with some narrow pliers and (if fitted) remove the circlip around the top pivot (not all versions have these). The cage and arms will slide off. If the adjuster screws are free, take them out and clean the springs and screw threads. Give everything a good clean, a smear of grease and re-assemble.
Rear mechs will also strip down but I've never done a 980. Jockey wheels come off, clean, grease and re-assemble. The cage should come off so that the tension spring can be removed and cleaned. Inside the body can be WD40'ed and cleaned out as much as possible.
Basically, just get as much muck off as you can, strip down as far as you can, clean, polish and reassemble with a smear of grease.
Today is the yesterday of tomorrow.