How can I sand an irregular edge to the same smoothness as the planed edges of my piece?
Short answer is you you don't. You can sand a live edge (UK: waney edge) if you want, but there's no reason you have to and many people want that natural surface as a contrast to the machined surfaces and edges.
If you need to smooth it out somewhat instead of sanding, which tends to level off high spots, the usual recommendation is to use a conformable abrasive, the two main choices being steel wool and nylon abrasive pads such as Scotch-Brite.
In either case you want to dust down thoroughly afterwards (don't be afraid to vacuum as well) but you have to pay particular attention with steel wool as the tiny flakes of steel can be harder to see in grain and other recesses before finishing, but after the finish goes on you'll spot little sparkles from any you missed without any difficulty! Additionally over time they can rust and discolour the surrounding wood due to a reaction between iron and tannins that may be present in the wood.