This is a tricky one, but a common issue to come up. English uses logical number agreement with groups rather than the strict grammatical agreement that many languages use. Usually you use a plural verb with groups if it is clear you are talking about the individuals in it, if they are acting separately. That's the case in your third example. But if you are talking about the group as a whole, then it should be singular. That's probably the case with your second example. But in your first example, you could say either, depending on whether you are emphasising the individual or group behaviour. It could depend on how you define "group of birds". But if you had said "flock of birds", where flocking stresses the way the birds interact with each other and take on a single shape, then I would use singular.
Also be aware that usage varies a bit by dialect. So American usage tends to go for singular in some cases where British English tends to prefer plural. It's not absolute either way, it's just a tendency, but you will hear it especially in cases like companies, governments and sports teams.