My plot was covered in couch grass, convolvulus (bindweed) and ivy (thankfully no marestail). With a combination of black plastic, glyphosate and sheer hard work its now clear. Took nearly a year all told, but this years winter digging has been a pleasure by comparison.
I started by digging and planting small areas as I cleared it, the 'diggings' were bagged and taken to the tip as it was mostly roots. Some of the plot I covered in plastic so I could essentially forget about it, and the worst bits I used glyphosate on. The glyphosate took about a few days to be effective (I used it in May, June and July but only on small patches at a time.) before digging everything in. The plastic covered areas were a pleasure to dig as by the time the plastic had been on for 6 months everything was dead and the ground underneath nice and crumbly.
I would say dig everything by hand and pull all you can out if you wish to be fairly organic and use no chemicals, and you can start now providing it isn't too soggy. Also cover what you can in plastic or heavy duty cardboard to stop light getting to the weeds, eventually they weaken and die. Glyphosate will have to wait as DD says until things are growing strongly AND you have at least 6 hours guaranteed dry weather.
Personally I would avoid rotavating until you can be sure all roots have gone, otherwise you will spread the problem and get very quickly disillusioned.
Good luc