From what I can get out of all the info out there, these are the capacities for the N52 (non-turbo 3.0l) 330i sedan:
Engine oil- 6.6l (7.1 US qts.) Specs 5W-30 Synth of API SL or higher. BMW High Performance Synthetic (in the US anyway) is a Castrol Grp. III but performs extremely well. GC currently in my sump.
Trans., Manual ZF, 6-spd.- 1.3l (1.4 US qts.) BMW Lifetime fluid 83 22 9 408 942 (MTF-LT-1) Another Castrol product available at the dealer for approx. $125 US for a 5l jug. Everyone seems to use a RedLine fluid, be it D4ATF, MT-90, or MTL. Personally I'm coveting the last few qts. of Specialty Formulations MTF Glide.
Trans., Auto., ZF 5-spd.- 9.0l (9.5 US qts.)for full fluid and filter change. Specs BMW lifetime fluid 83 22 9 407 807, which is Exxon (Esso) fluid LT 71141. This stuff is about $15-20 US a quart. Folks also using the Redline D4ATF but not nearly as many as with the manual. Lots more opting for the factory fluid.
If you have the GM 5-spd. auto, its 4.0l (4.2 US qts.) of BMW lifetime 83 22 0 024 359. This is a Texaco fluid, ETL 8072B. Haven't seen anyone mention changing this trans or using an alternative fluid.
Rear carrier (Diff)- .9l (.95 US qt.) BMW SAF-XO lifetime fluid. Strange, because mine calls for the same (E46) but I was able to get about 1.3 qts. in my diff. I wouldn't guess the carrier housing for the E90 would be smaller so figure on about the same. Almost EVERYONE eschews the factory stuff for RedLine 75W-90 gear oil. Again, small stash of highly revered Speciality Formulations fluid for me.
Hopefully if you"re asking because you aren't buying into BMW's silly "lifetime" fluid drivle. Good call.