Do you have to oil paint on canvas?

You can paint with oils on just about anything as long as it has a good coating of gesso. I paint with thinned oils on illustration board that's been attached to foamcore, masked around the edges and coated with three coats of a 50/50 water and gesso mixture. I don't like the texture of canvas because I thin my paint so much. Not even linen is smooth enough. Masonite works too. I don't use it because I think it's too heavy (I have to transport my art a lot), but I know several people who really like it.

Yes, lots of artists paint on masonite and wood panels. It would be a good idea to gesso them first, on both sides. But I know an artist who paints on wood panels that have not been treated. The question is, will they stand the test of time?

I paint on masonite all the time... but you have to gesso the surface first. you have to be careful of the corners as they damage easily... also larger pieces will warp (esp over like 16x20). i glue 1x2 bars on the back cut to line up flush to the edge. it is easier to have framed this way as well. also most art stores carry masonite like boards already prepared with a white gesso like surface for oils (try ampersand brand gesso boards available at blick etc). they have a slightly textured surface though, so if you want super smooth you can gesso yourself adding a few layers and sanding each one - they make boards that don't have any coating yet for this.

I have also painted with oils in watercolor paper. Just make sure is of good thickness. Wood panels, masonite, walls, and specially fibre board which does not bend like plywood,

I don't think masonite would work to well. Nothing to hold it in place but you can paint on wood used as a canvas.