I can't picture exactly the problems with your knives but I've had some very stuck tools before. I've received a Swisschamp with the tools completely or partially open because the previous owner found them too hard to close! I had to straighten and file smooth some bent liners first before cleaning. The small blade was so twisted it wouldn't close! Restoring it was a fun challenge and it's become a daily carry.
I reckon some people sell their knives because they don't think or don't know how to clean them. Local sellers online never mention stuck or stiff tools on used knives so I always expect the worst!
I always clean with warm water and dishwashing liquid and scrub the pivots and inside with a stiff brush until the tools open and close smoothly. Putting dishwashing liquid directly on the pivots helps. It can take a lot of patience. The small blade on a Camper was so stuck that I resorted to levering it open under the edge with a strong piece of plastic - it actually put a small ding in the edge!

I'll use padded pliers next time!
You want the tools to move smoothly after the clean. Then, only when the knife is dry do you oil the pivots. If you oil too soon you can get a poor result. In this case you have to start over. I've made this mistake and have had to soak the pivots in WD-40 to dilute the oil before repeating the dishwash clean.
I had to peen a loose pin once because the small blade opened right past its stop point. Again, not mentioned by the seller.

SAKs are durable things. Tools damaged beyond my repair have been rare. I can only think of a metal saw with a couple of broken teeth and a damaged scissor blade - yet they both still cut! Otherwise, except for an 84mm Vic that needs a new scissor spring and a Wenger with a slightly loose awl pin I've not had one yet that I haven't been able to restore to full working condition.
Good luck!