thistle in the garden & onion-like weeds in the lawn
Persistence is required, since seeds are almost certainly in the soil.
Thistle has an extensive root system so never rototill thistles. It is possible to hand dig seedlings in soft soil, if all root is removed. Do not allow flowering or remove flowers before seed forms.
More than one application of an herbicide is necessary to get rid of thistle. Paint glyphosate, active ingredient in Roundup and others to foliage or fresh cut stems when actively growing in the spring and fall.
See publication on thistle http://www.nps.gov/plants/alien/fact/ciar1.htm
Wild onions - You can manually dig out the weeds, if there are not too many making sure to get the bulblets out of the ground. Or you can spot spray a post emergent herbicide on the weeds when actively growing. Look for an herbicide that lists the weeds on the label and follow all label directions. To aid in the herbicide being absorbed into foliage, step on the onion foliage and twist your foot in order to bruise the foliage of the onion, then spray it with the herbicide.
See the attached publication for more information http://www.mdturfcouncil.org/admin/uploadfiles/tt-49-broadleaf-weed-control.pdf