This can be a particularly persistent weed vine. What herbicide did you use last year? We would suggest a non-selective systemic herbicide like glyphosate or triclopyr and probably repeated applications. You can cut the stems and paint or squirt onto fresh cuts to see if that is more effective than applying to the leaves. 

It is poisonous but relatively so. If you have pets or small children that may eat the berries you would want to remove those so they can't eat them. Also it would be dependent on the dose and size of the person/animal as to how toxic they can be. Brooklyn Botanic Gardens has an interesting article on it.  The birds and other wildlife love the berries so removing those before they can be eaten and spread could be helpful as well. 

If you just keep at it eventually it will exhaust its root storage and should stop returning. 

Emily

you're welcome!