Ok so I already created an Electrum wallet so then I just type the private key into Electum right?
Yes, just create a new wallet and select "Import bitcoin addresses or private keys".
Just note that, If the address you have in exodus is native segwit (an address starting with bc1), you must import your private key with the following format.
p2wpkh: Your private key
If your address is legacy only enter your private key or use the following the format.
p2pkh: Your private key
If I would like to make it more secure so that Exodus does not have the same private keys I guess I could first type the private key of my Bitcoin wallet into Electrum then, save the private key of my Ethereum address and reinstall Exodus or use an specific Ethereum only wallet and then import the private key.
The best thing you can do (only for your bitcoin off course, electrum only support bitcoin) is to create a HD wallet and sweep your fund into that.
To do so, select "Standard Wallet" and then "Create a new seed" when creating the wallet. After creating the new wallet, Click on "Wallet" at top of the window, select "Private keys" and then "Sweep".
If you enter your private keys in the new window, all the fund will be sent to your new wallet.
Note:
Keep the seed phrase electrum gives you very very secure.
The seed phrase give you the access to your HD wallet (a wallet with numerous addresses).
You can see list of all your addresses in "Addresses tab". (If you don't see the tab, click on "View" and make it available.)
Also, if you want to have your private keys, you click on "Wallet", select "Private keys" and then "Export".