Soap and water would not be my first choice for removing surface grime.

As well as dried and compacted dust, it’s likely to be a compound with some oil in it.

My approach would be to treat the metal and the wooden parts separately.

Make a sketch as you go, so that all the bits go back in the same order, then detach the wooden handles and knobs. Deal with those separately.

Strip down all the metal parts as far as you can, put them into a stout plastic bag without holes with a splash of white spirit – enough to soak the lot.

Leave it for 24 hours or so, and then brush an old toothbrush into the corners, rag it all dry. This should get the dirt either softened or removed. If it’s badly soiled, you may need to repeat this exercise.

At this point you can decide on your next steps.
If the finish is satisfactory, give it all a wipe with light oil and reassemble it all.

Good luck.