It is a sony str-dh590
That makes it easy. Run everything through the receiver. The 590 has four HDMI inputs and claims to be able to switch up to 4K
HDMI makes it simple Plug-N-Play. HDMI In on the receiver from each component, HDMI out from the receiver to the TV. That way you can switch everything with the push of a button on the remote. If you want to make it simple, use the Media Box input because that's what a Roku is.
FYI... sometimes it takes a few seconds for the video to synch after you change inputs (press the button). Don't be surprised if you see a few seconds of black screen when you're changing. Also, you may find the audio is a little out of synch. Most receivers and some TVs have and audio synch adjustment feature to compensate.
Brad