Arduino Mega serial in and serial out to OLED

Yup. The MEGA2560 has 4 serial ports.

(marketing commercial mode: ON) But Wait! There's More!
You can use any two digital pins and the SoftwareSerial library to set up another serial channel and so forth.

One BIG make sure you do with all of these --- connect ALL the grounds. Serial is 2 data wires and GROUND. Without the ground you can fry the hardware and even if you don't, the signals will not be reliable.