I agree with Simon Becker, I don't think you can find one with all of that. Try looking at Sensoray 826 or other models that are connected through PCIe so you can add several to your controller.
I've been using a daq from http://www.mccdaq.com/ and some from NI.com. All of them are USB DAq's. Your aplication has too many analog I/Os, Probably a modular solution will be the best for you.
cDaq modules can be plugged in cDaq usb system or cRIO embedded systems. It has up to 8 slots wherein you can plug all the requirements. For the 16 counters there are some fast digital inputs.
Another solution is to use PXI system: http://www.ni.com/pxi/
(I'm not from NI, but I'm used to work with its systems)