Weeds

OK, so I have been spending more and more time on battling weeds. And knowing your enemy is important so the topic of this post will be that.
Knowing your enemy is important but I have no clue what my enemies' names are. I got pictures so I will use those.
There are many weeds in my garden but three of them are really bad. First one is this tiny plant with bi-pinnate leaves and pink/purple flowers. It's pretty cute, except....it is the asshole of the garden.

Weed number 1. The ones with the smallest leaves.

It grows really fast and spreads its branches all around its root. Partially it does damage by practically laying on the ground and suffocating everything near it. Partially it climbs and clings to the branches and leaves of nearby plants and kills them that way, while thriving itself. Almost killed my old Jasmine plant. The poor thing has now been reduced to a forth of its original size. I have now cleaned out the purple suffocator from around it and in fact from everywhere else where I could see them.

pink flowers are just coming out

The way I kill them is to pull them out with their roots. Usually there are 4-5 long branches spreading out from one single root. So by following the branch to its hub and pull on all 4-5 branches at once, I get the root out too.
The second weed is, the notorious bamboo grass. My personal hate object. I have gone through the whole garden and pulled out as much as these as I could see. If possible, I have dug out as much rhizome as possible. And when cutting its leafs, I cut it below the ground (Maybe that is what I am doing wrong... I mean if I clip the stems above ground they kind of get hard and woody and new leafs don't grown out right away? While if the cut happens below ground it is moist and soft and new things sprout...)

This is how they start out

It is good I guess for erosion control but its rhizomes are literally everywhere and new leafs keep popping out. I figured that if I keep cutting its leafs, it would run out of energy and die. But the problem is that it has many many many leafs in the neighboring forest plot which is not mine and much bigger than my garden, and not maintained. So I can keep cutting leafs until next century but they keep coming. Unless I figure out a way to stop the rhizomes from spreading into my garden, I have no chance. In the meantime, cut cut cut the leafs.

Tiny new leafs sprouting from a stem that was cut before

I guess I can dig in root barriers. But the border line is 40 meters....

An old dried out rhizome I found lying around

With external influence cut out, then I can start dealing with the internal problem...

This is what it looks like when left uncut

It probably only takes one year of me doing nothing to turn my garden into the same state as the next door forest. I hate bamboo....
Weed number 3 is this really smelly piece of work.

The red-green spade shape leafs

It likes both sun and shade. It spreads through its soft roots that crawl right under the surface, and along edges. Both the plant and the roots smell like crap. Trying to pull out the stem with its long root is very difficult because it gets severed so easily. And even the tiniest length of root left unpulled sprouts new leafs next year and grows more roots. It really spreads far and fast.

Every time I pull one of these out I feel like puking

If only these three weeds were removed from my garden, I would feel much happier. Why is it that really smelly, annoying, destructive and most useless weeds are the fastest to grow and best at surviving while the useful plants like anything that I am now trying to grow need to be tended to extra carefully just to not die?