Not sure of the actual hardware buffer size, from the data sheet it looks like only a single character buffer. The Arduino board package implements a 64-byte ring buffer for send and receive on the hardware serial, and software serial appears to also use 64 bytes, at least for receive, I don't see a specific definition for the transmit buffer, but it may use the same ring buffer code.
Why specifically do you need to know?
MCUdude's MegaCoreX implements all four serial ports, and allows for easily changing the clock frequency of the processor if you really want it to run at 20MHz.