yeah, the first thing is to pull the hubs and check those bearings, might be OK but will need a good clean out, regreasing, and proper tightening ... all that crap on the joints is probably what makes them appear 'solid', may well find some zerks that won't even take grease [once you find them!] ... also note those tires aren't great, and the pitman end of the drag link has been rubbing on turns, will eventually rub the cap thin enough it'll come apart, hopefully not when you're at speed on a rough road - the tire might have a bad spot on the inner sidewall because of it as well, narrower, taller tires would improve things .... seeing the condition of things under there it's no surprise there's shaking at speed
Bill