I understand that Preset and Clear inputs are asynchronous inputs which means whenever Clock signal is low one of them can immediately set the output to 1 (Preset) or to 0 (Clear) (assuming they are active high inputs). But I wonder what happens when one of those inputs has been set to 1 when Clock was 0 and then Clock goes 1. Does J and K ovewrite Preset/Clear or they have to be released to let J and K affect the output?
If Preset and Clear are asynchronous, they will be effective regardless of the state of the clock.
If you set "Clear" active, the flip-flop will be cleared immediately regardless of the state of the clock, and will remain clear if the clock changes while Clear is held active.
A synchronous Set or Clear will only set or clear the flip-flop on an appropriate clock edge.