DEX/CEX: In times like this its best not to move around buying/selling tokens, unless one is a great trader 😉
OWL/Wallet: Metamask and OWL has it's own (online) wallet in owl.games
OWL/Ledger: Have no idea if that is possible. you probably know: metamask supported tokens can all be supported by ledger? or isn't it that straightforward?
OWL staking: Staking is done in their smart contract, if this can be on ledger, donno. expect it can't.

Note: OWL team is anon... one of the red flags in crypto world. but so far so good, they seem to be honest.