You can omit all kinds of things.
3:00 is three
3:15 is three fifteen
2:45 is quarter of if the context is "Is it 3?" "No, it's quarter of."
3:30 is half past three or half past in context, but never half to/of four
3:05 is five after three or five after in context
2:55 is five of three or five of in context, or two fifty five
3:01 is three oh one
And, as a general but often violated convention:
- am and pm aren't used in any context when there's a "normal" assumption
Examples: "My flight leave at 3" (normal), or "My flight leaves at 3am" (exception, or emphasis)
- am is often in the morning and pm is often in the afternoon or evening.
Examples: "My flight is at 3 in the afternoon", or "My flight is at three in the morning".
- 3:00 EST/EDT is three eastern, and the distinction between standard and daylight time is so bungled that people often trip over it.
- As noted above, of can be replaced with till and to throughout.