I am not sure how your built-in amp Overdrive works, but it probably won't mix well with the pedals, just run your amp clean. I have a 1980's Peavey amp which has its own built-in "saturation" effect which is a kind of waveform clipping circuit, they have several patents in that area. But they don't breathe as well as a tube circuit or a TS type pedal can, it just changes the waveform in a one-size-fits-all approach, like you can have any color Model T Ford you want as long as it's black, to paraphrase Henry Ford. The sweet sound comes from the edge of breakup, where your attack on the strings can send it over the edge, but a gentle pick strum remains pristine. Also, the EQ that you send into a tube pre-amp, or a OD pedal makes a difference, many prefer the top-boost or high-Frequency boost into the pedal so that the breakup occurs for the top strings and high on the neck positions while the low E and A remain fairly clean. I think you can adjust to whatever your preference is with a combination of clean-boost and OD pedals with careful attention to the EQ of both so the break-up and crunch has the flavor or color you want. "I want a transparent OD, well I want an invisible OD, heck I want an inaudible OD!" You can play with the volume control on the guitar, and the pickup selector, so you have some flexibility with how your pedals are dialed in to vary the desired sounds from using the controls on your guitar. It is a process.