Will this work on oxidized rims?

Yes, this product is very effective and doesn't harm the painted wheels or anodized surfaces, but a proper acid-resistant spray bottle is necessary, as is a rat tail brush and pail of soapy water to agitate and rinse off the acid solution and released brake dust. The first spray bottles I purchased "Chemical Guys ACC_121.16HD-3PK Chemical Resistant Heavy Duty Bottle and Sprayer (16 oz) (Pack of 3)" all failed to work after their first usage. I replaced them with "3 Pack 32oz. SprayMaster Heavy Duty Spray Bottles", which are holding up. The rat tail brush is "17 Inch Wite Wheel Spoke Brush Large" Keep dipping it into the soapy water and it will help remove what the acid softens. A mild brush on the outside of the wheels will suffice. I checked the MSDS and the active ingredients are phosphoric acid and citric acid, which are safer than hydrochloric or hydrofluoric acids. If the wheels are extremely coated with brake dust, then they might not become completely clean until the second cleaning. After that, once every few weeks should suffice.

Is this safe on any type of wheels?

Safe on most always test but I like it and use it daily..

can I use this on my aluminum wheels to get some hard stuck on grime off?

Depending on what is the source of the grime and how long it has been on the wheel, Speedy Brite may or may not remove it. Every case is unique and is a case by case scenario when it comes to something like this. As far as general aluminum wheel cleaning and maintenance, Speedy Brite is awesome!

Is this safe on powder coated matte wheels?

I don 't know if this is safe on your wheels but I do know that it's not very effective to begin with when using the suggested strength. It may seem inexpensive due to being diluted 3-1 or 4-1 but it isn't worth your money. It did a poor job removing brake dust and road grime from my clear coat wheels and was just as ineffective at cleaning tires. Caveat emptor, let the buyer beware.