If I transfer bitcoin into Trezor that has been on a paper wallet since 7-31-17. Can I still get BCH and BTG? Trezor has a coin-splitting tool, but it says that I had to have held Bitcoin in my Trezor on before August 1st.
The reason you cannot use the coin-splitting tool is that the private key of your offline wallet is where the new BCH and BTG coins were created at the time of the fork. By sending your BTC to Trezor, you are only spending the BTC part, the BCH and BTG are still associated with your paper wallet's key.
After your send the BTC to Trezor, you need to import your paper wallet's private key into a Bitcoin Cash and Bitcoin Gold wallet, and then send the coins to a new fork-specific addresses from there. Make sure to send the BTC away first before you start exposing your paper wallet's key, to ensure you do not lose the BTC in the process. See How to claim Bitcoin Cash & Bitcoin Gold from paper wallet for more information.
You simply need to own BTC on-or-before the split date. If you own the private key for the wallet that contained those keys, then you can create a BCH wallet with that private key and get an equivalent amount of BCH that you had in your BTC wallet.
Presumably, the paper "wallet" is either the private key, or an HD-compatible set of words you can use to recreate the wallet. I'm not sure how Trezor handles you recreating a wallet, but certainly it must let you manually specify either the private key or the mnemonic phrase that represents the private key.