If you're aiming for maximum efficiency, lose the relays. I think you'll find most of the mains rated ones will take a surprising amount of current for the coil.
Given (as others have said), I think you will need some hysteresis and in all probability at least a comparator for the "mains switch", I would use a solid-state relay to switch the mains side, as its "coil" will only require 1-2mA
The DC switching for your up-converter, using two relays seems unnecessarily wasteful too. You could do away with one relay for a start, by using one pole (as indicated by others) only, leave the (say) ground side connected on input and output and switch + through the relay contacts.
Check your up-converter - some (but not all) draw negligable current when they have no output load. If yours is one of them, you can probably leave the input connected permanently.
Again, not universal, but some supplies have internal output isolation so applying power to the OUTPUT doesn't actually draw any power or cause any harm. IF your supplies (both the PC supply, and the 12->20V converter) come into this category, you can dump the output switching relay entirely and just hard-wire the outputs in parallel
The other option might be to use FETs to switch your DC side. At the fairly modest currents you are indicating, the FETs will have very low resistance and waste very little power. Downside is that their "very little waste" will be for the whole time the system is running on DC.... so do your maths carefully - if the system will be running on mains for say 0.1% of the time, even 0.1 watts wasted in the fets may be more than the coil would take for the 0.1% of the time it is running...