Hi there! Make sure you canvas in Settings -> Video is 1920x1080, then open the Properties window for your Elgato capture source and ensure the resolution is configured to 1920x1080 there too. You can also click the Configure Video button in that Properties window to open Elgato's video settings window and make sure *that* matches. Then, in your console (or whatever you're capturing) make sure it's set to output in 1080p.
If you'd like us to provide further details on how to solve your issue, please post a clean log file. To make a clean log file, first restart OBS, then start your stream/recording for ~30 seconds and stop it again. Make sure you replicate any issues as best you can, which means having any games/apps open and captured, etc. When you're done select Help > Log Files > Upload Current Log File. Copy the URL and paste it here.
