Hello,
Baking papier mache can be helpful. I do it all the time, mostly because I live in a humid area and I want it to dry fast before mold starts to grow. Bake at a VERY low temperature (like 150 degrees), make sure to flip over the piece at some point also, because steam will accumulate on the underside. Be aware that if you place a very soft piece directly on an oven rack, the lines of the rack may imprint onto your sculpture. As far as how long to bake it, well, you just have to look at it to see if it's dry! If you overcook it, it will turn brown and brittle.
I do believe that baking does help the whole piece cohere better and therefore stronger. I never bake with linseed oil on it, I always just bake it as is and add other paints, oils, sealers, etc after. I cook food in my oven too so i don't want any nasty stuff to accumulate in there.