how to rid my garden of morning glories (which is very invasive)?
Ipomoea nil, commonly know as morning glory. although there are many species (20?).
Yes, a charming vine can self seed to easily, and can be invasive in some states. It's best to pull the seedlings as soon as seen if not wanted.
The species plants have escaped gardens and naturalized throughout much of the U.S. In a garden can self seed a lot! Once self-seeded in a garden can really take off. If you don't catch them when they're small, they will climb anything they get near, even bushes and other perennials.
And if you notice the vines returning some Spring without you having had to plant fresh seed, be vigilant! Look for stragglers outside your property, take personal responsibility for them, and pull them up or spray them with white vinegar or other non-chemical herbicide on a dry day. Because at your house they're probably among the best flowers you can grow. Next door, they're weeds. Note: please don't use toxic chemicals to control weedy plants.
Oh and one final note: There are white varieties of cultivated morning glory that are as annual in nature as their more familiar blue and purple flowered cousins. But if you didn't PLANT white morning glories and white flowers appear on morning glory-like vines, destroy every last one: That's bindweed, a noxious perennial that loves to strangle other plants.
Hope this helps.