IDC connectors for flat cables would likely not fit though, as there seems to not be enough space on the sides.
What kind of IDC connector are you thinking of? It looks to me as if 2-row .1" keyed IDC female connectors should fit just fine, since they go inside the black shroud you can see around the pins.
There were a type of connector where you crimped each wire individually, and weirdly there were no strain relief.
Sure, the standard crimp connectors that everybody calls "dupont," that come in kits like this. (I use them a lot.) The problem with them is that they're not keyed, so it's easy to insert them rotated by 180 degrees. (I suppose you could use a bit of glue or something to put a key on the connector, though.


These connectors do indeed have strain relief: it's on the pins themselves. Note that you need a particular crimper to get the strain relief to wrap properly around the insulation rather than to curl in and penetrate it, one that's "O" shaped rather than "B" shaped on the insulation part of the die. There's more information (and more pics) in
this blog entry by Matt Millman. (I learned a lot about crimping from him.)
As for the pinout, the way I usually approach this is to find an obvious ground point somewhere (on the power connector, on a 7400 part, wherever) and use a continuity tester to find the grounds on the connectors. Then power it up and see if any pins on the connectors are providing power (+5 or +12 V); these are either actual power supply pins for the device at the other end or handshake signals that are active. If you see any -12 V you know you're dealing with RS-232 levels, otherwise it's TTL.
For the rest, it depends. If you can identify any of the chips on the board you can trace from the pins, often through buffers, to the chip pins and see what they are. Microcontrollers often have just a few pins that can be used with their internal UARTs. If it's all a big mystery, you probably have to figure out how to get the device to generate some serial output and use a 'scope on the various pins to figure out where it's coming out and at what rate.