Understanding Operational Transconductance Amplifiers
The most important point to note is that the input diodes and \$I_{bias}\$ pin allow you to operate the amplifier open-loop with a current input signal. If you are apply a low-level differential voltage input or operating the amplifier closed-loop, you may ignore the diodes and bias pin all together.

A Operational Transconductance Amplifier (OTA), is often just a differential input pair followed by a current-mirror. One branch of the diff-pair is mirrored to the high-side supply. The alternate branch of the diff-pair mirrored to the low-side supply. Both current mirrors are connected to the output pin of the amplifier.

So, if the differential input voltage is 0 V, each branch of the differential pair has the same collector current (equal \$V_{be}\$ for \$V_{diff}\$ = 0). Hence the output is sourcing and sinking equal values of current resulting in a net output current of 0 A.

The input diodes are not just ordinary diodes, they are geometrically, thermally, and process matched to the input differential pair transistors (also a good chance they are actually diode connected transistors). Such that the current following through each of the diodes is scaled value of the current its respective element in the diff-pair. This allows you to apply an current input-signal and still operate the OTA open-loop. 

If you go through the derivation for a current input signal (or voltage signal with high source resistance) the gain of input signal to output current becomes a simple linear function of \$I_{abc}\$ and \$I_{bias}\$.

You can find full derivations in many of the app-notes such as the one listed by tek,http://www.ti.com/lit/ds/symlink/lm13700.pdf