Oregano is invasive, but that's if you forget about it for a few years. It will VERY EASILY reseed itself and spread and I think it makes for a great ground cover, fragrant and easy to pull out. Mine took over my "herb bed", but it isn't like weeds that cannot be pulled out. You can control it. I forgot about mine, except looking at it, and it has taken some time to jump the cement border, but I'm pretty sure that it was the seeds that grow outside of it. It will give some weeds a run for their money.
I would recommend planting oregano around other vegetables.