Ordinary lacquer thinner works great for cleaning pretty-well any type of paint from an airbrush, but it’s best to use it immediately after you finishing painting or when you wish to change colours. My Paasche VL has been in service for almost 40 years, using only lacquer thinner and a pipe cleaner after a painting session.
I have a pretty good supply of Pollyscale paint still on-hand, in my opinion, the best model paint ever, even better than Floquil, the brand with which I started in the '50s.
For Grimy Black, choose your brand of black paint, then simply add some other colours to it - depending on the amounts used, red will shift the black to brown, white to grey, green to DLGE…which is pretty close to Grimy Black.
I recently built this BowserA-5 for a friend, then painted it using Pollyscale “Brunswick Green”, although with a coat of Glosscote, it does look like it’s pretty-much just black…

…a little weathering does shift it from straight black, though…

Grimy Black, which was, I believe, a Floquil name, always struck me as having a green tinge to it, so I’d start with a black of your brand choice, then add some green and perhaps a little grey or even a little less white.
I’ve had pretty-good luck mixing colours to match pre-painted items by using a “brushload method”. For Grimy Black, place 4 or 5 brushloads of black on a non-porous disposable surface, then add a brushload of green - mix it in, then, if it looks like it needs more green, add a brushload. Keep track of the colours used and number of brushloads of each