Is there any way to check which wards skins I own? Or I only can see them after locked my champ in the lobby before one game starts?
The Loot tab will only show you your ward skin shards, which you need to upgrade with orange essence to activate (click to enlarge):
There's currently no place to see all your ward skins besides the lock in screen. The easiest way to look at them is to create a custom All Random game. This will give you one full minute to look at your ward skins; then you can simply quit: