Graynomad:
Is this a one-off, if so I guess you just buy the boards. If not you'd be better off making your own shield.
No, he will be much better off buying the products he linked to in the first post. A good brand for serial/ethernet bridges is Moxa and for a one-off unit you may be able to pick up one or two surplus units from e-bay. The cost for the functionality they provide is reasonable. If you're after a DIY project to learn from, it's a different story.
8 channels at 38400 baud is 307200 baud (307kHz). Then to multiplex this back out to UDP or TCP, you will typically need at least twice the combined input baudrate for your output channel. Then what about traffic in the opposite diection? This is going to be a stretch for an AtMega. The bus interfaces available on AtMega are I2C (max 400kHz) and SPI (max 8Mhz as master and 4Mhz as client). If you want to interface externally multiplexed USART's, I2C is not likley a viable option due to the limited bandwidth. SPI is the ontly interface that will give you sufficient bandwidth both in terms of input and output. Still, the combined inpout/output bandwidth plus overhead is a stretch.
Doing 4 channels with a AtMega2560 based designed may be an option as they have 4 built in USART's plus SPI. You will then need to double the hardware for 8 channels including power supply and ethernet bridge, add line drivers (to convert from TTL to RS-422) and still you have the challenge of writing the software to handle the total IO required. A nice enclosure wouldn't hurt either.
There are some low cost (less than $30) single channel serial to ethernet bridge modules available for diy'ers. This may be an option as output can be connected to a low-cost ethernet bridge/hub. Still you're looking at adding the bridge/hub, cables, power supply, enclosure and also RS-422 line drivers as the modules are likley to be TTL only.
All in all this is a demanding project with lots of uncertainties until you have worked through and verified a complete design with both hardware and software. The ready-made units may then not seems as expensive as you first thought.