Bathe your pup as often as needed IIRC the general thought is that shampoo strips oils from the hair, so it's best to bathe only once every week or two. However, there were definitely times as a puppy when I bathed Mia on consecutive days, according to how dirty she got. It may be sub-optimal if you're aiming at a show coat, but it won't do any harm.
Yeah, imo if you think to yourself "you're stinky", then it's time for a cleaning... I wouldn't let my hygene get to that point, so why let your pet. I try to apply the same hair rules since humans and poodles have a hair coat. 1 weekly washing w/ shampoo... spot rinse or full body as needed. Again, shampoo strips the oils.
If more then Basil's feet are gross, then we just go through the full routine (minus shampoo). She's very clean after rinsing off in the shower, and a blow dry. The whole process takes us less than 30 minutes for a clean and cuddly poodle. Yes please.
Depends on what the stink is but I used Show Sheen for horses. Spray on comb into the coat then dry. It helps repel dirt. Also helps reduce tangles. Then I spot treat with it in spots where we sit or lay in something or use waterless shampoo. I used to call him my long legged P.U.del... now I call him my Padoodle as he's out grown the P.U. part. (He's a purebred Poodle it's just a nickname).
If he's just stinky from rolling in the dirt or peeing on himself, then definitely give him a bath. However, stinkiness can also be a sign that he has an ear infection. Galen's ear infection smelled like fermenting corn to me.