Here is the Firepod listed on ebay. They don't make it anymore, but they have a new version which is the same thing you linked to just a little more fancy so now you can get these relatively cheap off ebay. It's basically 8 inputs via 1/4 inputs or XLR inputs (microphone cables) that have preamps but that's not going to affect anything with you. Also 2 of those inputs have phantom power so if you use a condenser mic, you'll be able to power it, but if you use a dynamic mic, it doesn't matter. The mics will benefit from the preamp.
This thing would work perfect because I checked out the back of your drum machine and it has a R/L outputs so you would run a 1/4 cable from each of those to the firepod.
As for your synth, I have a Alesis Micron and have messed around with synths and they usually have R/L stereo 1/4 outputs on them so you can run those into the firepod as well.
The drum machine, synth, and mic will use essentially 5 inputs giving you 3 left over.
This thing works and is powered via Firewire and you can hook monitors into the back of the firepod via XLR or 1/4 cables.
From what I understand this thing will do everything you want it to do and you could probably get it off ebay for around $200-300.