Skipping the obvious uses of pitch shift and eq...
Editing can be your friend. You don't necessarily need to use the whole sound when building the voice. Selecting only the sections that contain the key timbres your looking to add, and placing them in as "accents" can be a useful trick. For example, a full horse whinny may not be what you need, but a chunk of just one of the oscillations they produce can be a nice lead in to the next component (maybe to a segment from a howler monkey or high pitched, raspy, bird). Experiment with combining granular pieces of sounds with related timbres. You can create some really interesting sounds in a linear fashion, even in only one layer.
If you're going to try using a vocoder, my suggestion is to combine sounds that have a similar sonic trajectory. The closer they match in frequency shifts (they don't have to be exactly the same frequencies, I'm just talking about percentage shifts up and down), the better the two sounds will mesh. Something I did a few months ago makes a decent example of what I'm talking about. I had a set of human vocalizations that I wanted to use to modulate electronic interference noises. I built a patch in Structure that let me play out the electronic interference to get the timbres I wanted (through mapping the raw electronic sounds to my MIDI controller keys), and pitch bend them to match the pitch trajectories (through the MIDI controller's joystick). I took those intermediate sounds and ran them through Waves Morphoder with the original human sounds as the modulator.
Those are my suggestions. I'm looking forward to seeing what interesting techniques other people here use.