I would like to know if there is a software that can generate a waveform where I can adjust modulation and pitch visually over time. I'm trying to make basic animal sounds.
Most well featured modern synths allow you to do this. Look out for graphical enveloped such as these in Absynth:
Absynth might be a good choice for you.
I'd also check Andy Farnell's work in PureData in this area too. If you want to get into this seriously, then being able to patch custom systems is really a must (imho).
There are two good wavetable synthesizers:
2) Waves Wavetable Synthesizer: http://www.waves.com/plugins/codex#codex-synth-in-depth-tutorial
I have used both and both are absolutely amazing!