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".
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.
If your address is legacy (an address starting with 1) only enter your private key or use the following format.
As stated by DireWolfM14, you can also export your seed phrase from exodus and import it into electrum.
For exporting your seed phrase from Exodus, click on "Backup" and then select "View Recovery Phrase".
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 doesn't support ethereum) is to create a HD wallet and sweep your fund into that. Be aware that for sweeping the fund, you will have to pay fee to miners. Because you actually move your coins to a new address.
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 (a series of words) electrum gives you very very secure. The seed phrase give you full 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 this tab, click on "View" and make it available.)
Also, if you want to have your private keys, you can click on "Wallet", select "Private keys" and then "Export".