I'm not Norwegian, but in Dutch we do a similar thing. If the pan was laying upside-down, I think 'ligger' would be appropriate, or if the fork was standing straight up somehow, you could use 'står'. What might help is if you image a set of eyes on the object, and then see if it's laying down or standing.
That said, at least in Dutch, nobody would care that much if you use the wrong one. I doubt I would even personally notice.
Coming from German, I'd say that if something is taller than it's wide (or about the same) it would probably "stå".
Or alternatively, if you can tip something over, that means it "stands" if not it "lies".
Not 100% applicable though because, at least in German, plates (e.g.) "stand" on the table.
If you type 'kjelen' into Google Translate it says boiler, and if you type 'sauce pan' into Google you get pictures of a boiler. Therefore, 'sauce pan' must be another term for boiler, which means 'kjelen' also means boiler. Also, I asked my Norwegian husband and he said he would use the word 'boiler' in English.
It is perfectly correct, grammatically. But you could put any verb in there and it would be grammatically correct: the saucepans are dancing/sleeping/laughing on the table. All correct.
Whether anyone would actually say it is another matter. I'd probably just say the saucepans are on the table. If pushed I'd probably say sitting rather than standing, but if I did say standing, everyone would understand.
A saucepan is a cooking pot, normally with a long handle, sometimes a lid, that you use on the stove top.