So I've been doing a lot of heavy erratic work on muscles that were previously a little lazy. And I do get Delayed onset muscle soreness, which is nice because it definitely feels like muscle is being built, but doesn't make me want to exercise very much. Is it a good idea to exercise through it? Or should I take a break? Maybe not do any strength stuff?
It also depends how sore you feel. I remember some time ago I tried something new and I pushed myself too hard. I was sore all right. It was a pain to put clothes on or use bathroom ;-). Now with this kind of soreness I decided to simply wait and let the body recover from the shock. When I have more typical, light soreness I try to move but with no pressure. If I feel like it, I will do lighter workout, if not - I will just skip it that day.
A lot depends on what your intentions are. You have to realize that the soreness is due to the muscle fibres being damaged from the workout. The fact that they are damaged and not yet repaired means that they aren't as strong as they were before the exercise so you won't be able to work them hard enough to stimulate any more growth, at this stage anyway. A light workout can increase blood flow which can speed repair but it is usually counter productive to engage in any heavy work. Bear in mind that depending on the degree of damage done repair can take 7 to 10 days to fully recover and be stronger. If your lifts continue to increase it is a good indication that you are recovering sufficiently between workouts. However if the next workout isn't as productive as the last it's a good chance you aren't fully recovered and probably should have a rest or light day. I recommend you read "Body by Science" (John R. Little, Doug McGuff) Dr McGuff explains in exquisite detail what happens inside the muscle.
There's a piece of old wisdom about this that has always stood me in good stead: to make the soreness go away, do a lesser version of the same exercise that made you sore. Beyond that you'll have to ask all the great training enthusiasts we have on this site.
If Paleo has taught me anything it is to listen to your body: I would rest
Remember it is quite an "unnatural" to have X muscles really out of shape or weak and then obliterate them with exercise... If you were raised a hunter-gatherer you would have been working and strengthening all your muscles in unison your entire life.
I bet if a tiger or lion wakes up with really sore muscles they chose to sit that day out!
When I was a kid (early 20s) I used to just push through the soreness and keep exercising. Eventually the soreness would abate after your muscles worked out the lactic acid and you got enough rest each night. Usually took about a week to 10 days of sore workouts. I'm my mid-thirties now and I'm a big believer in proper rest periods, but I think a light workout through the soreness will keep blood flowing through the affect area and hasten muscle repair and growth. That being said, I typically work hard through the soreness for a few weeks and then give myself about a week off with some easy resistance training every other day: heavy weights, low reps, to increase strength and density, then back to the grind.
I've always just worked through DOMS. As long as it's only DOMS (not an actual injury), and you're giving yourself at least one rest day between workouts of the same muscle group I don't see what could go wrong.
I work through DOMS, but I make sure that I'm properly mobilized before doing it. The main risk that I'm aware of, is that you will change your form to avoid the pain. That way lies injury.
There doesn't seem to be any other risk associated with it, according to wikipedia.