I take in 2 g Flax Oil twice/day, 200 mg ALA with every meal, and 2 g CLA with 3 meals/day. I also cook my eggs in Olive Oil.
I can't say anything for certain (because I'm no expert), but I think all my fat intake has helped me to retain strength during my latest diet (<70 g of carbs/day). I might even be gaining strength on some exercises.