Firstly - I have no idea what I am doing.....

I just purchased a Pioneer 5070 tv with 2 hdmi outputs.

I also have a Panasonic receiver that is a year or 2 old - but it has NO hdmi connections or DVI. Only composite and Svid.

I am getting a DVD with hdmi. I am getting a DVR through comcast with hdmi. Do I need to upgrade my receiver to utilize the hdmi features on my other, new stuff?

Your TV has two HDMI "inputs".

Run the DVD and DVR directly to the TV for video and audio via HDMI (when using the TV's speakers for audio).

If your A/V receiver has optical or digital coax inputs, run either of those connections/cables from the DVD/DVR outputs directly to receiver for Dolby Digital or DTS.
If your A/V receiver does not have digital audio inputs, then run an analog audio cable (red/white) from the TV's fixed audio output for stereo (or Dolby Pro Logic if the A/V receiver has DPL).