That's a bit complex to answer. Trezor has an automated tool for extracting Bcash and BitcoinGold for you (and both coins are supported by Trezor wallet). But that will only work if you already had your coins on the Trezor before the forks. The problem in your case is that, when initializing Trezor it will generated a new seed (24 words) and you move your old coins to new address (generated with that new seed). There might be one situation in which case you could use the extraction Tool, but for that you have to import your old seed from your old wallet (with the coins before the fork dates). Did you have a BIP-39 wallet before, with 24 words? If yes search the Trezor documentation to recover a wallet with a saved 24 words seed. Recovery will give you your old wallet on the new Trezor.
I did try to get my bitcoin cash using electrum cash but it would not move through the process after I pasted in my private keys. Any other ways to get the bitcoin cash before I move to the trezor.
Private keys? or the 24 word seed? Those are two different things. (you cannot import private keys into Trezor). For other ways: it's best to ask specialized Bcash forums. (try reddit or bitcointalk).