Back when I was still actively modeling (20 years ago and more), all I really had access to was enamel paints for the base coat and wash. I found that if I let the enamel cure for at least two weeks, I could apply an enamel-based wash without the base coat 'crazing'. Nowadays, I would probably try acrylic base coat and enamel/oil wash, or vice versa, just to save some time. I never got a smooth wash appearance until I started using oils, but oils required an application of a clear flat coat to get rid of the shine, and I never liked too many coats of paint. I found that I could get a reasonably smooth effect by using my usual enamel wash, followed by vigorous drybrushing with the base color (or a slightly faded version of it), to sort of cloud over the open areas and 'smooth' the edges of the wash, and bring out detail. It took some practice to get it smooth enough to be 'subtle', but after a while I got pretty good at it and ended up with some nice looking models (armor).
After trying oils on aircraft and finally getting a really smooth wash, with the ability to just rub the edges smooth, I think that's what I would recommend instead, if you don't mind the additional coat of clear flat, or if someone else can recommend a way to get an oil wash to dry with a flat finish.
As for mud, I found two techniques that worked very well. One was to make a somewhat thick wash of a light tan color, and take a very fine brush and hand-paint individual 'splashes' around the sides of the vehicle - with about the transparency of 'dirty water'. It's a little tedious, but I always enjoyed the finishing tprocess the best., so I found it fun. Combined with pastel dust and some drybrushing, this gave me some very realistic results, without going for any thicker mud application. Just take a look at some dirty vehicles out on the road or a construction site, and you will see how it's done. One drive through a puddle, and this will happen to any vehicle.
The next step above that is the opposite - give the model its liberal dusting with pastels (grind the pastel chalk on a piece of sandpaper, and work in the powder with a brush - but only on the areas you want it), and then take a fine brush, wet it with water, and 'streak' the pastels away from the upper parts of the vehicle. This prodices the final, realistic dirty effect. It's a really cool effect with vehicles that have big vertical sides, like the Bradley or Sherman. You just can't touch the model anymore, and I never was able to find a flat over-coat that preserved the look, so once the pastels were on, my models became permanently "hands off".
I had great success making actual 'mud' by mixing regular talcum powder with the enamel color of my choice, and applying it with the toothpick I mixed it together with, or whatever I had handy. It makes a nice, thick mud and seems to last forever. A good way to do it is to make two different colors - dark and light, for wet and dry mud - and apply one first, and the other afterward. I always put the 'dry' mud on first, in thinner layers and covering more of the model, followed by select areas of the darker 'wet' mud, to simulate thicker deposits in the places where more mud would accumulate. Again, check pictures and real-life construction vehicles for good tips on how it 'should' look.
Good Luck,
Brian B.