I'm going to need to paint my house soon - the eaves, overhangs, and trim. Most of it doesn't need to be scraped, but I do need to clean off the 20 years of grime. What do you recommend for cleaning it?

TSP. And gloves.

Use a brush or a sponge to scrub off the dirt. A sponge might shred a bit on the rough parts so be aware.

Pressure washer

I use a combination of TSP and Clorox Outdoor mixed with water. I scrub with an outdoor broom type brush and power wash it off. Works like a charm.

I think a pressure washer with Simple Green's pressure washer solution should do the job. I've gotten a lot of stuff off with that.

Home Depot has this version. The one I have, which may be a fence wash, I got at Grainger.

https://www.homedepot.com/p/Simple-Green-1-Gal-Oxy-Solve-House-and-Siding-Pressure-Cleaner-Washer-Concentrate-2310000418232/306781778

You can rent a pressure washer if you don't have one. Beats the heck out of scrubbing, though I'd spray a highly concentrated (1:1) amount on the area with a pump sprayer, agitate it a little with a scrub brush, then hit is with the washer for best results.