The problem with running is that you really need to ease into it, or you're going to get hurt and then not be able to ride. It's tough to accept a 20 minute run as a workout when you are used to 3-4 hour bike rides being a workout. I just ran for the first time in about a year last week, and I had trouble walking for four days because my quads and calves were destroyed. I only ran 2.5 miles. I did the same run last night and am sore again, but not as much. If I ramp up the mileage though, I know I'm gonna be injured.
I find the climbing gym to be a great way to get exercise off the bike. It seems no matter how sore my legs are from riding, I have no problem climbing. It's a totally different workout, and it's really fun. I try to time it with the weather so that I ride on nice days, and climb indoors on shitty days. I count climbing as a rest day, although I usually end up with one total rest day where I just sit on the couch.
I might ride if I'm sore, but I just take it really easy. None of my rides are ever hammer rides though, so I don't really have any advice there.
If your diet sucks and you know it, just start eating better. It's really not that hard. Eat more stuff that's better for you, and less stuff that's bad. I would suggest you read Eat to Live, but I basically gave you the premise of the book in the previous sentence.
It sounds like you just need to take some time off the bike and do some easy rides and then you'll be fine.