I need to place two of these transformers in a case. How close am I allowed to place them? Can they touch each other (of course, they will be electrically isolated)? Is their orientation with respect to one another important? What kinds of closest placement types do you suggest?
The importance of the placement varies depending on what each one is being used for (power, audio, relative signal strengths, etc) For example, a potential disaster is placing a low level audio input transformer next to a high level output transformer. A similar issue could be the power transformer next to an audio input (or possibly output) transformer.
Generally, to minimise coupling the cores should be placed at right angles to each other (flux lines at 90 degrees to each other), and as far away as is practical. You will see this done with input/output/power transformers in many audio amplifiers.
For power transformers, remember there are also heat and vibration considerations, so solid mounting/damping and ventilation needs to be looked at. I agree with Tony that touching is not a good idea, so if it can be avoided do so.