This sounds very much how I experience sciatica (could be piriformis syndrome, as never formally diagnosed). Although, I do not experience pain down into the calf, merely the thigh.
As for you, I find temporary relief with variations of several of the Stretch Therapy movements - piriformis stretches (for me, the floor p.stretch is best), hamstring stretches (elephant walks are great, but I have to be very careful getting into it, if it is very twitchy; bent leg pike stretches with gentle movement), and hip flexor stretches (wall hip flexor stretch with plenty of support).
For me, to maximise relief, and minimise exacerbation of "rebound" effects, relatively short and very gentle periods of limbering are best; done periodically throughout the day.
I haven't done it for a while, but I also really like @Craig's Psoas Lying Relaxation: