I think they can be decent general or sometimes general-specific exercises. It depends on the needs of the athlete, though. The log, I like. The Axle... I guess it's fine. It will function mostly like a thick barbell, so grip will be trained. Tires are a decent conditioning exercise. It kind of felt like sumo deadlifting to me. Stones could be supplemental -- like RDL's. I think you'll find that stones are somewhat like front squats -- you won't really be sure if it's targeting the right things for PL. Events like Yoke walk, and to some extent Farmers, have even less transferance.
Oly's... same thing as above. Some things will carry over. Some won't. I wouldn't expect it to be very specific, though.
To use a big word, you have to look at what each event/lift develops in terms of the biodynamics (i.e. skills -- is the technique of the movement something that will develop/improve the technique of the competition lift) and bioenergetics (does it develop a particular energy system that is important to further development of your competition lifts). The psychological aspect of it being enjoyable and entertaining is important as well, but we need to keep it within the confines of improving the competition results (which I'm sure you understand completely).
