When I just had my period there was a strange odor that has never happened before. I thought I was over my period till me and my husband had sex and that caused me to start bleeding again and it was black. I have had back pains that causes pains to shoot down my legs everyday all day long. Is this something I should be alarmed about?

Very dark menstrual lining and blood means it's been exposed to air and oxidized. There's nothing wrong with that, although it's probably old, and for some reason is taking a while to come out. Low back pain and pain down legs are often associated with menstruation, hormone fluctuations, fibroids, tipped uterus, other organs collapsing onto the uterus and bladder, infections (you'd have a fever), cysts, and all sorts of reasons that make nerves sensitive. Doctors often have a tough time finding a cause. They usually start with a pelvic exam and an ultrasound. They recommend pelvic tilt exercise, walking, keeping your bowels moving every day, healthy diet. Maybe an incline board. Exercise in general, and possibly yoga.

(I had pain down my abdomen and the inside of ONE leg for 30 years that turned out to be a sacral nerve, only diagnosed correctly by a chiropractor. Again, some lower torso pain is very difficult to diagnose.)

Oh, I forgot some of the reasons for odor, such as trichomonas and other very easily treatable little buggies. But it might just be the smell of old tissue/blood.

I think you should see a doctor as soon as possible.
Odor, black (old) blood, pain in back and legs... yes, most assuredly you should see a doctor.
I hope all goes well with you.