You don't say what type of seacocks you have. Locked up Blakes taper fit types can be shifted with a sharp tap from a piece of timber, after which they need to be drawn and checked for wear and ground in if necessary. You have to be a bit more gentle with ball valves, especially the plastic ones which can shear easily. Gate valves can also be hard to budge and you might do well to think about replacing them. As to grease. I have used Duckham's Keenol for past seasons and found it very effective. Ordinary automotive type stuff is not up the the mark.
If they are Blakes Seacocks, get some Blakes Seacock Grease. Goes a long way. I grease mine at the beginning of every season and have never had them stuck. Still on the original tube of grease after 11 years!
Do not know really about valves, had to replace them recently, used Blakes grease for them
seized seacocks (Blakes ?) should become undone if you tap them with a hammer and wood. Use automotive grinding paste to clean them, works great. Remove it all and put Blakes grease.
Nico