The possibility for all of the mentioned birds to live all in a same area is because they are all specialized and occupy a certain niche in the food chain, thus not standing in each others ways when it comes to competition for food.
All of these birds have adapted to be able to survive in their respective environment, developing characteristics that will enable them to be superior in something. Through natural selection, the individuals that were performing better, got the chance to mate, thus the offspring was better adapted and stronger in its niche of the food chain.
The robins and the blue jays are birds that are very opportunistic in their food choice, thus giving them greater flexibility and ability to survive, they mostly feed on worms, insects, fruits, vegetables, so they have a big menu.
The finches are specialized in eating nuts and seeds, thus avoiding the competition with the previous two, thus having that food type for themselves.
The owls and hawks are both birds of pray, but the owls hunt mostly at night, while the eagles during the day. Also, the owls prefer to have rodents as their pray, while the hawks are mostly eating other birds, thus not standing in each other's ways.