Yes, you need to calibrate for each combination of source device and display input that you intend to use. You may discover that some inputs or some source devices work well with a single set of settings, but you can't KNOW until you check.
The problem of course is that using something like Avia is only going to work to calibrate a DVD player through some display input. So what do you do for the inputs that are going to have something else connected?
A professional calibrator will use signal generators -- for instance a generator that puts out an HDTV signal that can be fed into your HDTV receiver to calibrate that receiver into your display. But you don't have that.
Most people start by calibrating their DVD player connected the way they intend to use it and then use the resulting movie images to train their eye as to what a calibrate image LOOKS LIKE. Meanwhile they temporarily hook up their DVD player to the other inputs and use it to get a candidate set of calibration levels for each other input. This helps make sure any "torch mode" stuff is turned off in the display for that input. However, whether those levels are useful with any other device connected into that input depends on how close that device is to the DVD player in the levels it generates. You can get your devices closer by setting them all to the same sort of Black Level (the lighter 7.5 IRE setting or the darker 0 IRE setting for what gets sent out when the source content wants "Black") and by setting all of your source devices to the manufacturer's defaults for whatever the manufacturer describes as the picture mode which does the LEAST to the source images.
But in the final analysis, since you can't easily get calibration test images on screen from your other devices, you have to tweak the levels for those other devices BY EYE -- constantly referring back to what your calibrated DVD player shows when playing movies as your gold standard of the quality you are trying to match.
In the plasma forum, there's a thread called the "steaming rat" thread which talks about adjusting calibration by eye and the sorts of things you might look for when trying to decide what to tweak next. Specifically he's talking about making your DVD images look better than what you achieved with your calibration DVD, but the same technique applies to doing eyeball correction of levels for any source device.