Not sure about adding lime, will reduce pH, and I always think the higher the better for seeing off nasties? Don't know, need a boffin . . . HF, where are you?
Definately dig over. I do this regularly to ease compaction, and just to freshed it all up. I do it really rough with a garden fork, and leave huge s*ds and clodds. The girls just love it, and get their heads right between the tines if I'm not careful. Lots of worms, and then they've got all the fun of straightening it all out again when I've gone.
'Fishy' does sound nasty. Something decomposing?