Bathe your dog to cut down on odors in the house. A monthly bath is usually sufficient unless the situation warrants an additional bath.

Brushing out a burr is not always possible, but there is another way, as opposed to just hacking it out in a chunk. It still cuts it out, but in a less traumatic way for your dog's coat.

Take a sewing seam ripper, and pick the hairs around the burr until it can be pulled out.

To prevent burrs from becoming encased again, a spritz conditioner will keep his coat nice and slippery, and any burrs will brush out easily.
Bobbi Panter Snarly Dog Spray  or Happy Tails Aromatherapy Spritzer Detangler are both great for this!