If sewer gases are coming out of the pipe that used to be connected to the part of the sink where water drained out of the bottom, the pipe has not been sealed off or the pipe has been broken in the process of removing the vanity.
Most municipalities will not permit an unlicensed person to dabble in plumbing. A plumbers license is required to make sure that sewer gases do not enter the home. Sewer gas is very dangerous to your health.
I suggest you get a permit for the plumbing work. Have an inspector check the work that has been done on your vanity connection. Then, hire a licensed plumber to complete the sealing of your vent piping.