the slimey stuff sounds like your mucus plug. Everything you've described sounds like your body is gearing up for labor. It shouldn't be too long now. Good luck!
I also think it's your body getting ready for Labor. Good luck and let us know.
All normal parts of the lovely third trimester. Your body is getting ready for labor though WHEN labor will happen is a mystery. It could be in two days or it could be in two weeks; these signs are not indicative of labor occurring sooner rather than later. And since you are still preterm it would be best for baby to stay in until week 38; many babies born before then wind up in NICU with respiratory complications.
*Meaning you should contact your doctor. I just reread your post too and green discharge with an odor could be a sign of infection. I would go get checked out to make sure all is well!
How is the baby? I imagine you had the baby not long after this post and it is now May 3rd.