After brushing, I used Murphy's Oil Soap on the table and most of the wood. The drawers (not shown) and their runners looked to have been treated with some type of shellac many years ago. They cleaned up reasonably well so I decided not to strip this off.
Although I'm currently concentrating on the table and the treadle mechanism, I did take some tentative steps on the cleaning and de-greasing of the actual machine. Using Formula 409 I gently cleaned the steel cover plates and then, even more gently, tried the main body taking extra care over the decals. I am pleased that these seem to be in good condition under the layers of grime, although more work on this is required after I finish off the woodwork.