ghostrider

Oil sticks are oil paint in solid form. The same basic pigments and drying oils that are used in the formulation of tube paint are combined with wax and rolled into a crayon. They cure and dry permanently on fabric, just as they do on canvas (which is just another type of fabric after all). Cure for several days to a week before you heat set them for the best results. (Do not heat set before curing and do not skip the curing step.)

Oil pastels are very similar to oil sticks but with one critical difference: the oil used in formulating oil pastels is generally a non-drying oil. Like pastels, they never dry permanently and will attract and retain dust and grime because of the slightly tacky surface. It's the reason pastel art work is always covered with glass while oils are not. Heat setting will not change this fact.

Shiva oil sticks have the highest pigmament concentration and that is why they are the most preferred for use with fabrics. It is also why they are at the higher end cost wise. There are several other brands available and student grades of many, including Shiva. Student grades use less pigment which reduces the cost to make them and therefore the price. If cost is a concern, it would be wiser to go with a lower grade oil stick than to use an oil pastel for work on fabric.

ETA: One other note, because oil pastels are made with non-drying oil, they may continue to permeate fabric just as they do when used on paper. Fixatives are used on papers, but you wouldn't want to use them on fabrics.