I know pulling weeds is tedious but if you go at it and get them out before they flower and then form more seeds you will have a leg up on the problem. Get as much of the root out as possible. Also, you can pour a mixture of hot water and vinegar on them to kill them. Here's a link for more info about that:

http://forums.gardenweb.com/forums/load/permacult/msg0521511914969.html

Your bird of paradise looks like it needs dividing - It's a bit of chore but can be done. Here's a link for that

http://www.gardeningknowhow.com/exotic/dividing-bird-of-paradise.htm

I hope this helps