It seems that many invasives are more nutritious than our day-to-day counter parts. If I can eat them they can be used for variety, extra say minerals, and time available to put into other plants or endeavors, its a win-win! I know many acquatics are edible but I am having a harder time eating them, but if I could impart knowledge to others so they can enjoy them, it may help prevent some overtaking an area. I am now looking at most plants now as a solution for something. Is it edible or could it be mulch, etc. I look forward to reading and learning more. I just made a small mason bee hostel using last years japanese knotweed branches. I plan to locate them throughout the yard. Maybe one or two for the neighboring yards.
My wife is on the Soil and Water Conservation board and just judged an Environthon as it is called. One problem a team had to deal with was a wild type of mustard that I forget the full name of. Anyway they created a Salsa and made a recipe book for it figuring "the best way to deal with it is to turn it into something edible and make use of it." For high school students I love their ingenuity. Good for them (and yes they got high marks and may well go on to the nationals).
Yesterday I was a farm meeting and smooth bed-straw came up, which is so irritating to me. Smooth Bed-straw is an invasive species here that thrives with low PH levels. It is easy to kill because you just have to get your PH levels up with lime, but our local lime quarry quit selling to farmers 10 years ago leaving us to import it from Canada. That is prohibitively expensive, so the root problem is; we had a resource, it is now gone, and so bed-straw prevails. If we could only convince the quarry to start selling to farmers again, we could eradicate this issue easily.
I mention this because with most evasive species they thrive under certain conditions, find out what they thrive on and eliminate it and they are done for. They can also be tell-tale signs of what your soil needs for amendments. When I see fields teeming with bed-straw I know they need lime; queen abbes lace...they need nitrogen...no soil testing needed.
As other commenters have mentioned, there are many invasive species with exceptional nutritional value, either for us, or for birds, insects and other mammals - which are also part of the story of how they spread (pollination, seed dispersal, etc.) Some that stand out for their particular nutritional qualities are Autumn olive (Eleaganus angustifolia), one of the richest known sources of lycopene (the antioxidant found in tomatoes), Japanese knotweed (Polygonum cuspidatum), whose root contains high concentrations of reservatrol - the antioxidant component of red wine used to treat heart disease, milk thistle and other thistles are highly regarded in the herbal medicine community for their liver cleansing and tonifying abilities, and all parts are edible. Garlic mustard (Alliaria petioloata) is another nutritious invasive member of the Brassica family (with those cancer-fighting sulphur-based compounds also found in kale, etc.) Multiflora rose and sea buckthorn were introduced for their food value for wildlife (and we can eat them too - both have fruits that are very nutritious to people). Kudzu is edible and medicinal - all parts (the roots is used to make arrowroot powder to thicken soups and stews). One of the lines of research I have undertaken is to look into how the invasive plants are used in traditional food and medicine making in their recent places of origin, as this gives a lot of insight into how they can and should be used where they're currently proliferating!