How do I kill plants the healthy and organic way?

currently live with my grandmother and she has a garden that REAKS of stinky and unnecessary plants. I tried to convince her to remove them and we'll plant veggies and flowers..stuff we can actually use rather than have stinky leeks and other nonsense. How do I get rid of these plants the natural way so that I can start planting edible plants without her thinking that I had to do something with the demise of the stinky plants??? Please help, she is even getting neighbors interested in leeks and stuff!! I would really apprciatte it if any solution you guys give me wouldn't end up hurting her or me in case we eat some leeks..just in case she wants to taste the plant to make sure it's really gone bad,k? Thanks a bunch