Vinegar - straight. I had a dog with incontinence, and when she would accidentally pee on a rug, I would pour vinegar, let it set for a few minutes, rinse, and wash in the washing machine with normal detergent. It absolutely neutralizes urine. If you don't get it out - they will go back as an "approved" place to go. Vinegar is the only thing that works, IMO.

Musty/Old people smell (no offense to old people - I'm one of you!)

I recently bought some vintage hankies from eBay, and when I received them, I was dismayed. They smelled like "Old people smell".

I washed them using the "Sanitize" setting on my HE machine, with extra oxyclean - in the prewash as well - and it all came out. I was so happy. Had never used this setting before, but came away a firm believer that water temperature plays a big part in clean-ability. I think it also helps that I have soft water, too.