I have a 2010 Chev Cobalt with the variable valve timing. The previous owner had unplugged both the vvt solenoids when the service engine light came on with those codes. He said it has run okay since only stuttering sometimes. Is there any chance of damaging anything with them unplugged in the short term or long term?

Interesting question, as to whether it might cause damage.....not sure.....

However, by disabling it, you affect two things....performance and emissions.....

The performance part is evident by the stumbling.....

Many VVT engines don't have an EGR valve....so how are exhaust gases introduced to reduce NOX?

Normally, on the intake stroke the ex valve is closed and the intake opens, and sucks in the air/fuel mixture as the piston drops and creates a vacuum.....VVT eliminates the EGR, by changing the position of the ex cam, under the right conditions.......so what happens is, instead of the ex valve being completely closed on the intake stroke, it is slightly open and the vac created by the downward piston sucks in the air/fuel mix, plus some of the exhaust gases....the result is the same as if an EGR valve existed....