Dig out as many nettles as you can, following the runners as far as possible, then next spring dig the new shoots out again, then later treat any further regrowth with glyphosate when it's got plenty of leaves.
A well-constructed trellis (really stout posts and good quality trellis) should withstand the wind and create a baffle. You could choose whatever density of trellis suits your requirement to let light through and choose some hardy climbers to break up the appearance. Too many dense climbers would increase the wind resistance and compromise the stability of the panels.
It is autumn here, so I'd start now. You need to make a start before the weeds die back and disappear. There's a bit of hard work, but that's why we have gardens!
Search 'glass balustrades' and you will find a lot of ideas that might be suitable. We have friends who have these on first floor decks and they are pretty good, but not as cheap as a plant.
Any chance of a pic?
I can't see what makes this garden 'unusable'.
Young magpies like to hang about together from this time of year onwards.
Yew every time!
I think it might be wise to do a bit of this at a time - 150sq m is quite a lot of rubble. Perhaps try to do the third of the plot nearest the house/in the sun or the least challenging bit. It will give you a sense of achievement.
Get someone in with a mini-digger - not too expensive and very quick.