Two current carrying wires kept at a distance will repel each other if they have currents in opposite directions. In the case of a current carrying square loop, would two opposite sides also repel each other? I think there would be a repulsive force which would cause a strain in the other two wires. Can somebody rectify this?
Yes, running a current around a wire loop creates Lorentz forces that act to expand tbe loop and stretch the wire.
An alternative way to think about this is in terms of the magnetic pressure. The current produces a magnetic field passing through the loop and this in turn is responsible for a magnetic pressure $B^2/2\mu_0$ (in SI units and which is equivalent to the energy density of the magnetic field).
According to the wikipedia page cited above it is possible to pass enough current to force the wire into a circular loop (the minimum energy configuration) or even to stretch and break the wire.
Yes, they two loops would repel/attract each other based on their orientation. In fact, a bar magnet works in a similar way.