For solving edges on 7x7x7 cubes, what's it called when you orient the edges first? That is, you take all the white edges and put them into edges together so their white sides are all correct but their other side is scrambled. Then they're easy to fix using slices. Same with the yellow edges. And then orient the last four edges before solving them.
The basic idea is that once the edges are oriented, there are only 12 possible ways that they need to be permuted. That is:
(8) One correct and a cycle of three, i.e. (234), (243), (134), (143), (124), (142), (123), (132),
(3) Two cycles of two, i.e. (12)(34), (13)(24), and (14)(23),
(1) Correct,
which means you only need to know two algorithms for finishing them off, or just one, i.e. (123), if you're willing to use:
(12)(34) = (123) x (143).