Need to get rid of ingrained dirt and rust

Alright, I will admit to being an idiot and not doing the regular cleaning of the bike due to my own failure to do so and heavy workload over the summer. My KLE500 has got alot of rust, including on the exhaust pipes along with dirt that ingrained that the regular cleaning stuff I use can't get it off. It's a bit of a dumb question, but any decent ways I can get the rust and dirt off without damaging the bike?

Here's some image links showing how much there is.

Sorry for the lopsided shots, I had to upload them from my phone.

Clean loose rust off with soft wire brush. Paint with rust eater, then appropriate colour top coat. Hammerite smooth is good.

There's no quick fix here. There are two ways to approach this . One is to remove all loose material with a wire brush , Scotchpads or wet and dry paper. Mask off one area at a time and spray paint using a primer and some satin or gloss black or silver . Hammerite , as previously mentioned, is very durable but Toolstation do a cheap range of paints that will look OK. Option two is to take the whole bike apart and properly restore each part before reassembling it. Depends upon what your long term plans are really. If you want to sell it for top dollar you will have to spend more time and money than you will ever get back. By the way your KLE looks to be in about the same condition that my ER5 was in when I got it.

I can recommend Ronseal NoRust paint. I used to paint my boat trailer with Hammerite every year, then one year I couldn’t get the usual paint and bought the Ronseal instead. That was 11 years ago and I’ve not painted them since. I used it on a 70’s Vauxhall to paint the suspension parts 5 years ago and it’s just as good now.

Hammerite is good but it’s not as good over existing corrosion as the Ronseal stuff.

Clean loose rust off with soft wire brush. Paint with rust eater, then appropriate colour top coat. Hammerite smooth is good.

Which is how I kept the rust at bay with my KLE500. The brush has copper coloured bristles, I used Kurust and Hammerite black paint. I hand painted pretty much everything. I even painted the spokes and was surprised at how well they came up. I had the bike for about 4 years and did it twice with a few touch ups in between. Make sure once you paint the chain adjuster slider that you put plenty of copper grease on the inside to stop it welding itself to the swingarm. I painted the exhaust with very high temp paint, but ended up getting a new one as it rusted away.

I got the swingarm, pillion foot rest brackets and bash plate powder coated. These are the photos I took to advertise it for sale;

I even hand painted the front fork and the black part of the brake disc. The spokes looked like the spokes in your photo, so you can see they come up well with hammerite.