The bitcoin wallet Android App doesn't recognize wallet.dat file of bitcoin-qt.
And bitcoin-qt doesn't recognize key file exported from bitcoin wallet android app.
How to make them use same wallet? Thanks.
Neither of those wallets are designed to remain synchronized. You should not be attempting to access the same bitcoins from both wallets simultaneously. Doing so is likely to lead to confusion at best, and loss of bitcoins at worst.
Instead, you should send bitcoins from one wallet to one of the addresses in the other wallet if you want to move bitcoins between the walllets.