Can I make a full backup of my phone with Odin and without root?
Odin is Samsung-only, you're right.  (And as far as I know it isn't for all Samsung phones either, though I could be wrong on that.)  Since Heimdall is, as far as I know, just an unofficial port of Odin I would assume it's the same, but I've never used it.

Odin3 has a "Dump" function that I had never used.  It seems to be disabled in v1.8x and v1.7, but not in v1.52.

I just tried it in v1.52 and it didn't work.  You hit the Dump checkmark under Option, select an output file via the Dump button under File [Dump], then hit Start.  Odin will say "OneNAND Dump Start" or similar as it backs up the device.  It only backed up 1 KB of something before halting, though.  Odin just sat there without giving an error message.

You might have different results with a different device (I have a Vibrant).  I'm also wondering whether my Ext4 lagfix might be affecting this.  Perhaps later I'll flash to stock 2.1 and try again.  Edit: No change on stock 2.1 JFD.