For how long can a raven stay airborne (a week or more)?
Can't be very sure about ravens but the maximum recorded flight duration is of Common Swift — 10 months.
Alpine swifts also remain airborne for up to 6 months.

Pigeons can fly up to 1800km in a long flight. From this article (pubmed):


  In the United States, the longest pigeon races involve flights of 1800
  km and, because substantial financial rewards accrue to the owner of
  the fastest pigeon, there is severe selection for those pigeons that
  home the fastest.


Wikipedia article on pigeons says that they can fly at 80km/h but I suspect because the other wikipedia page on flight speeds says that average flight speed of peregrine falcon is 65-90km/h. So assuming that average speed of pigeon is 60km/h it should be able to fly for 30h. According to this paper, the speed with minimum power consumption is 8-9m/s (~30km/h). At this speed they should be able to fly for 60 hours. In the same paper it is estimated that the maximum continuous power output is ~10.5 W; if a pigeon has 11g of stored fat (per 400g body weight — assumptions from the same paper), and given the calorific value of fat — 38kJ/g, it can fly upto 38 × 11 ÷ 10.5 = ~40h. This means that the best trained ones can perhaps manage to fly for 2.5 days straight.

Now ravens are heavier (~3 times heavier) but are more aerodynamic and can fly faster. However, I guess they cannot perhaps fly 7 days straight.