Trying to hook up my Onkyo stereo TX SV 313 Pro to my TV model Vizio E601i-A3

That TV has analog audio output so it's easy.
Connect the DVD to the TV with HDMI.
Connect the TV audio outputs to any input but phono (if the receiver has one).
Check the TV manual to see if the output has to be turned on. You may be able to set it to variable in the TV menu. That would allow you to use the TV remote to adjust volume.