First, please check that model # for your Zenith.
Yes, you can run HDMI from both the satellite box and the dvd player through the receiver and out to the tv via HDMI.
(the Sony receiver has two hdmi inputs and one hdmi output, correct?)
Another option, which some folks like to do, is to send the video signals from satellite and/or dvd players to the television and send the audio signal to the receiver.
Video is sent via hdmi or component cables.
Audio is sent via optical (toslink) or digital coaxial cables.
Either system works. Both systems will give you a proper set-up. Give them a try to see which you think is best.
cyberbo60, often you will find in the owner's manual a hook-up section that describes the options as good, better, best. Take your time, it will be worth the effort. Good luck.