I've recently learned some of the tools of GPGPU and parallel programming (OpenCL, CUDA, C++ AMP, and OpenMP) and have been looking for more things to tinker with.
I know that there are purpose-built USB ASIC devices for fast bitcoin mining ("block eruptor"). Is there a way to program these via OpenCL or another GPGPU-like API? It seems that although they may have been built for a specific purpose, they might have computing power that can be used for other tasks.
I think you are clearly miss-informed and messing things here.
OpenCL, CUDA, C++ AMP, and OpenMP: are programming languages that run into devices that can be programmed (CPU/GPU/FPGA).ASIC devices are chip (Hardware) designed for a specific purpose. They are fast, cheap, and low power but that is because they have only 1 function (the HW is NOT configurable). The one you designed in the manufacture process.
So, no. You cannot use OpenCL to program an ASIC.