Yes, oxidation is a good way to develop "nutty" character. My oxidized Meadeira batches take on that "nutty" aroma which is common to Madeira wines and Sherries. If you like something in that style, it works well.
Oaking meads can also produce some "nutty" flavors. Of course, you can use nuts and some recipes call for them. I've not tried Mahlab, but it seems to provide some of that to the cherry meads where it is used according to those that have tried it. I've read people have used acorns in some recipes, so I think there are many ways to produce "nuttiness."
As for bitter - thats easy. Excessive tannins, whether from enologic tannins, or from prolonged extraction from seeds will give you bitterness. I've made batches too bitter by leaving too many pits in my mango batches. Keeping berry batches on the fruit too long, or doing heavy pressing of the fruit will give plenty of bitter. The white pithy stuff under the skin of an orange is very bitter and I work to avoid getting it into batches. Hops can be used.
Really it all depends on what you want to make, and once you decide the direction you want to go, you can find ways to accentuate the things you want (maybe, if you're lucky, that is unless your name happens to be Schramm or Oskaar ;D ).
Medsen