You can use fantasia Wig Shampoo which I love for my wigs
I don't get the oily feel as well but it could be from touching the wigs with your hand, or it could be environmental.
I get this about 3 weeks straight of wearing my hair.
How to wash your LF/Wig/Unit's
Put tepid water in a small bucket about a gallon
Put 3 oz of Wig Shampoo into the bucket
Brush your unit free of tangles
immerse your unit into the water and swish it around for 3 minutes
lift and swish again for 1 minute
remove and empty bucket
put another gallon of tepid water into bucket for rinsing
swish hair around for 1 minute
lift and hang on shower head/bath faucet/window handle to dry hanging
DO NOT COMB/BRUSH/HAND COMB/BOTHER HAIR, LET IT DRY THROUGHLY
If you feel after the first time you'd like to add watered down light conditioner feel free to do so but rinse well or it will feel like build up.
enjoy!