What if the patio is uneven with several joints. Will the paver overlays work on this or should I go with taking up the concrete and put in base work and pavers?

My experience is in highway and bridge construction so you have to take my suggestions with a grain of salt. There are latex modified overlay concrete materials which can be used in small thicknesses-and they are expensive I bellieve, but probably cheaper than a whole new concrete patio removal and replacement.
Concrete pavements are oo often overlayed with hot mix asphalt to get rid of irregulaities (smell should go away in short order) but probably not easy to find highly qualified people to do it).
Maybe sand under pavers would work if you can keep it confined and deter washout.
Don't know what type of stone you are considering but you would basically make skateboards out of the pavers. Stone dust- maybe?
Good drainage is also imperative if the patio abuts the home.