How many resonance structures does the oxalate ion have?
Resonance structures are not real things. As also indicated by rbw, they have weight on the actual compound. Simpler example is ozone.

http://www.wou.edu/las/physci/poston/ch222/pdf/Ch08-s12-part2.pdf

From the first slide second image there;


you can see that the actual molecule is none of the "resonance" structures, and both bonds between leftmost and rightmost oxygen atoms with central oxygen atoms have equal lenght, and it is between 1 bond length and 2 bond length. 

The general idea of drawing resonance structures is, after predicting the most appropriate ones, when you superimpose them and average the bond lengths you will be very near to see the real chemical bonds lengths. 

This is straightforward with ozone, oxalate or carbonate etc. but things get complex with increasing atoms, though. 

And wrapping up and also answering the question you posed, you should look atoms as if they are all unique, like oxygen 1 oxygen 2 oxygen 3 and oxygen 4. Flip the molecule and you will NOT get the other one, this is not like isomerism. It is just to predict the electron cloud density around atoms of a molecule.

Hope this also helps.