I'd like to offer some suggestions for displaying your wooden birds:
Many of the birds in our house that are waiting for a new home are perched on the corners of our many window sills, either looking outside or looking inside. They look good in the light and sometimes are nicely siloueted by the brighter outside light.
The horizontal wood or rock perches with two or more birds on them tend to be placed on horizontal surfaces in our home: one of my favorites - the red sandstone base and weathered and "redded" desert wood perch with its six birds is sitting on top of our television set. Another similar grouping is on our fireplace mantle, and others on bookcase shelves and on the surface of our kitchen bay window. Also, some of these birds and their horizontal perches have found a good home on our window sills too.
The hanging birds are a lot of fun to place. Many were found on our Christmas tree this past season. Some had red and/or green hanging ribbons and others had the nearly invisible nylon fish line. The birds looked very much at home in the tree. Others were hung and will be hung from indoor plants - some from the branches. Small pots can have wires bent with a "hook" to catch the hanging loop so that the bird(s) can have a place among the plants in your house. If you have any hanging lamp-pulls, a bird could be a decorative and functional end of your pull. If so, I'd suggest gently filing the birds sharp beak a little bit. In our kitchen bay window, I hung upside down some red berried branches with some hanging birds among them, "eating the berries".