What conditions could be expected to occur if one or both inputs of an op amp are left floating?
I'll interpret your question a bit more broadly, since the results with one or both inputs floating are unlikely to be working usefully. 

In general there are two categories of op-amps, bipolar ones which have significant bias current that is of guaranteed direction, and FET or MOSFET-input types which have smaller bias current of undetermined (and possibly changing) direction. 

In the former case you can generally predict the output state with one input left open from the datasheet, provided the other input is kept within the common-mode range. For example, the LM324 has a bias current of 20nA typical. That means that if you leave the inverting input within the common mode range, then the non-inverting input will float up outside the common mode range in the positive direction and the output will be close to the negative rail. If the inputs are swapped, the output will be close to the positive rail. 

If both inputs are left open the output state is harder to predict and may or may not be consistent for a given op-amp design. The schematic is published for the LM324, so one may see that the output ought to be low, but it isn't- it goes to the positive rail, so the schematic is not complete. 

The second category of op-amps will have undetermined (and possibly changing) output depending on leakage, pickup, temperature, humidity etc. 

In any case if the op-amp has proper supply voltages will be "working" but if you are feeding it garbage signals (floating around, picking up noise or outside the common mode range) it will provide garbage of some description at the output.