Odd layered cubes can have no parity. I think you are talking about last two edges algs.
I originally thought they were parity as well, until it happened on my gigaminx and I asked how to solve the parity, and people told me it wasn't a parity.
Can you be more specific?
Assuming you are talking about last two edges, then 3 is all you need, and 2 of them are 4x4 algs. I use three. and never have to apply them more than once, since I edge pair a certain way, to make sure only 3 cases can appear.
I use the single match/flip - 4x4(Last two edges)
The single edge flip - 4x4 (OLL parity)
and the edge flip/swap - 5x5
found on
this site
I may use different algs than those ones tho.
Hope that helps.