I get this too, but only periodically, and only when overtrained or i've been running a lot of hills (early XC season). This has gotten much worse with age, i don't remember getting it much when i started running in late 20s and into mid 30s.
One "cure" for sore quads is to "vaccinate" them with some downhill running. This invokes eccentric contractions in quad muscles and causes and lots of DOMs over next few days, Do this once a week for a few weeks and report back. Find a long hill 1k+ and do a few repeats, or more repeats over short distance. Google this for details. This is common Boston marathon training technique.
Lots of threads/articles on cold water therapy for sore muscles, some say it works, some say id doesn't. Sit in bathtub with painfully cold water, for up to 10 mins. Don't take shower to warmup, let body warm up naturally. This is painful if ice cold, and your hands will get cold about 20 mins later. If you heart starts beating irregularly (e.g. skipping beats) you've overdone it, relax, don't panic, it will reset itself (at least mine did!).
Warnings and other points:
1) downhill running can cause knee problems, start easy.
2) if your quads are already chronically sore, you may have to rest up before trying again.
3) validate basic stuff - is your weekly mileage ramped up too quickly? Are you sleeping/drinking enough? Are yo eating enough? Don't drink too much alcohol, inhibits protein synthesis and other recovery issues.
4) don't OD on pills for Vit C and other antioxidants (e.g. resveratrol) this will inhibit the bodies own adaptations, and exogenous resveratrol has been shown to inhibit Vo2max gains. Don't worry if you're eating a lot of oranges/kiwis, natural sources won't mess with adaptations.
3) Make sure you're eating enough protein, RDA is pretty low, 54g for 154lb man. Some "experts" think that's way too low for endurance athletes and recommendations are for >1g per pound of bodyweight. Sounds like a lot, but no where near 300-350 that body builders consume.