I have used oven cleaner on the pistons in the past and it works well. You can really use any good metal cleaner and finish off with a fine wet & dry with soapy water.
In the head chambers, just scrape the carbon off & finally clean with a wire brush in a power drill.
It is surprising how quickly it all gets 'black' again though.
With the engine running, it used to be considered good to pour Redex down the carb(s) with the engine at around 4000 rpm. That made it smoke a bit, but it got the muck out. We used to do this as part of every 'pre-rally' tune up.