How to get vegetable oil out of cloth?

I made some cloth napkins and we use those instead of paper towels. So over time some of them have soaked up different oils, like vegetable oil. Some of them seem fine, but others seem like the oil has stayed in the fabric. There's the dingy-ness (which I will bleach out if need be) but also wonder if some of them are less absorbent now. I've heard of "stripping" cloth diapers before. Would that work for oil in napkins, too? 

In case it matters- they are two layered. One layer is diaper flannel white and the other is 100% cotton. TIA to anyone who can help!