Reference for (odd-hole,antihole)-free graphs?
In fact, it is relatively easy. Instead for studying independent set problem in (odd-hole,antihole)-free graphs, we take complement of the graphs and try to find a maximum clique in it. Thus it becomes maximum clique problem in (hole, anti-odd-hole)-free graphs.

In section 2 of the paper "Triangulated Neighborhoods in Even-hole-free Graphs" by da Silva and Vuskovic, they stated that Farber first shows 


  There are $O(n^2)$ maximal cliques in any 4-hole free graphs.


Then their main theorem stated that


  There are $O(n + m)$ maximal cliques in even-hole-free graphs, and all the maximal cliques can be found in time $O(n^2m)$.


Since we are dealing with (hole, anti-odd-hole)-free graphs which is clearly even-hole-free, finding a maximum clique takes at most $O(n^2m)$ time.

4-hole-free are critical to these kind of results like a poly-time algorithm for $\overline{K_{2,m}}$-free graphs, so the real challenge may be studying independent set problem in (hole, anti-odd-hole)-free graphs instead, which becomes the maximum clique problem in (odd-hole, anti-hole)-free graphs.



Edit:

Oh, another thought came out. (hole, anti-odd-hole)-free graphs are almost weakly chordal in the following sense: since 4-hole-free implies there are only anti-holes with size 4~7 remains (any k-anti-hole with size > 7 contains a 4-hole), and it is also anti-odd-hole-free which restrict the size of anti-holes down to 4 and 6, it is almost no holes/antiholes in the graph! Thus a poly-time algorithm seems plausible for such graphs.