Our thought so far is to speak English when we are all together, Swedish between me and the baby, Italian between my wife and the baby.
That's the way recommended by all sources I know of. I.e. be consistent with your use of language when you talk to the child - each parent (and other persons too) use one and the same language - preferably his/her mother tongue - at all times, as much as possible.
On average, bi- and trilingual children develop their language skills slower than others, which is quite understandable as they need to process a greater amount of stuff. However, as usual, there are wild variations in skill development. E.g. we know a child with a Spanish father, Finnish-Russian mother, currently living in Hungary and attending an English school (earlier they lived in Moscow for a while). He is a bit over 7 and speaks all five languages quite fluently. This happens, but is definitely not the norm :-)
So be patient, talk to her a lot, relax your expectations - she will most likely learn all three languages sooner or later. You are also right not to throw in Japanese into the mix yet - I would start that only around school age or even later, when she already has a firm grip with the first three languages.
Be prepared that she will most likely develop preferences, depending on how much each language is used, and by whom. E.g. our children are bilingual (I am Hungarian, my wife Finnish), and the elder is fairly balanced between the two, because she started to talk earlier, and spent more time at home with her mom. The younger, having been slower to develop, and started at kindergarten earlier, has significantly weaker and more passive Finnish skills. Obviously the wider environment has a strong influence in this once she starts to spend more time outside of home. So at kindergarten / preschool / school age you may want to take opportunities to upkeep and strengthen the other, non-local language (which would be Italian in your case, at least for the time being). Our children attend to the local Finnish Sunday school, to learn more about the culture, spend time with Finnish speaking friends, practice reading / writing etc.
Check out this related thread too - it has useful suggestions and references, also details about the checkpoints, i.e. what to expect realistically from your child at a given age.
