All I can say, Ed, is to return to factory settings, then very carefully look at all the options you have set for your BIAB sound card.
If it truly is a loop, then something somewhere is pointed back to itself.
I just looked a the page for the
IK Multimedia iRig Pro Duo and I see it has a USB connection to connect to your computer, as well as MIDI in/out (although I've never seen 1/8" connectors for MIDI before), 2 line/instrument inputs, and two outputs (which would generally correspond to left/right stereo).
Please let us know how you have everything wired. It seems to me that you should connect the iRig to your computer via USB, and that becomes your sound card interface. That should establish both audio input/output and MIDI input/output.
In BIAB, you would select the iRig USB-in as your input device and the iRig USB-out as your output device. If you want to hear anything, you need to either connect headphones to the iRig or connect an amp to the line out connections. if you use MIDI, then you can select the iRig MIDI in (to receive data from a keyboard for example), but if you are only using VSTi's or DXi's for MIDI output, then you don't need to select the iRig as your output device (but if you do, it will by default sent MIDI data out that connection to the keyboard or external hardware MIDI device connected to the iRig.
In ASIO4ALL, you should go to the expert view (click on the wrench icon) and make sure your input and output ports are set correctly, as ASIO4ALL may be seeing multiples (for example, it may separate out the headphone out from the line-out, but I don't know without looking at it).
Don't know if this helps any, but if you are truly getting a loop, then something is connected back on itself somewhere. For example, if you connected the line-out from the iRig to line-in of the onboard computer soundcard. Not saying you did, but just an example.