You do use your muscles differently in running than cycling, and your movements are definitely going to be different. DOMS (delayed onset muscle soreness) can be from lactic acid buildup, it can just be using the muscles in a way they are not used to be being used. Make sure you are doing good pre and post run stretches. I like to lay on my side, reach back and grab the top of my foot, then try and straighten my leg, while sucking in my gut to protect my back.

When you stretch, try holding it for 30 seconds, then relax, then 45 seconds, then relax, then one minute. This will help to get the muscle to relax. You can also do 20 minutes of ice, with at least 40 minutes off.
Just give the quads a chance to get used to doing a new activity. I'm assuming you're in fairly good shape from riding, so you are probably just pushing yourself a little to hard with your runs. You could also have allergies or a slight cold that could cause a mild strain.

Of course there's the old stand-by.................You're getting OLD!
Happy riding, and if you ain't 19, remember you ain't 19 anymore!