Petroleum products can be very difficult to remove from clothing but it can be done. First use the hottest water you can. Simple green is an effective degreaser, but tends to foam a bit, it may cause your machine to suds up and will require extra rinses. Or you could soak the clothes in a hot simple green solution in a bucket, rinse in hot water and then launder in hot water with some washing soda(sodium carbonate), or borax. You can also add STTP(sodium tripoly phosphate if you have it, if not then I wouldn't buy it just for this. Use hot rinses if your machine will allow it. If you normally use fabric softener then skip it, as it make it harder to remove petroleum odors because it coats the clothing fibers. Next run the clothes thru the dryer and repeat the process if needed. Drying in the dryer adds lots of heat which helps to boil off the volatile petroleum components which is what is giving off the odor. Simple green is a fairly gentle degreaser and it rinses well, but like all degreasers it is more powerful than normal detergents alone, thus make sure you rinse, rinse, rinse. A last resort could be dry cleaning, yes it will be kinda pricey to have a whole load of laundry dry cleaned but the solvents used by dry cleaners would definatly remove any petroleum compounds, and it would be cheaper than new clothes. For what it's worth I work in a machine shop and my clothes always get oily from machining oils etc, the washing soda alone removes the smell and any oil stains that might be present. Hope this helps.

Try soaking everything in the hottest water you dare (considering the fabrics) and Dawn liquid dish detergent. Just by the plain Dawn, no "oxi" or other bells & whistles.
Dawn is what they use to clean wildlife after oil spills, such as the famous BP spill in the Gulf of Mexico a couple years ago.

Scrub gently, rinse thoroughly (or the sudsing in your washer will be a nightmare, then wash in washer.

I cannot guarantee this, but a lot of mechanics' wives use Dawn to pre-soak their husband's clothing, and they swear by it.

Cavimum has a great idea here, never thought of the dawn trick, I know some who swear by it though.

I vote for Dawn also, given the constraints by the OP.

1. Rewash items with your favorite detergent.
2. Use 1 cup of baking soda with 3/4 cup of vinegar in the first rinse.
3. Use your favorite fabric softener in the second rinse.

This is what I do to remove the scent of Lestoil which is an oil base all purpose de-greaser.