Wahoo! I think I can answer your questions Daisy - but I'm sure Longy, Weezie or someone else more experienced will follow and I hope they'll correct me if I'm wrong.
I think you can add the sod to your compost pile - but the bigger the clumps are, the longer it'll take to break down. Clumps of soil won't be a problem - I often add leftover potting soil, or garden soil from when I dig a hole, etc., to my heap. Again, the smaller the clumps, the faster your pile can work. Be careful with old vines. Depending on what they are, and whether or not they've gone to seed
. If you want to be sure they're dead, lay them out on the pavement in the sun for a few days, then add them as your 'brown'. The chemically treated weeds
I'd say throw out. Reason being, if the chemicals don't break down in your heap (and I'm not sure if they will or not), they could hurt your flowers
when you add the compost to your gardens. They might also hurt the wormies, and or the microbes that will work on making your compost into black gold. You especially don't want to add it to a compost heap you'll be using around any fruits or veggies. Personally, I'd just chuck them in the trash. Now for some REAL expert advice...Longy? Weezie? Bueler?