What type of grass could be used for a very shady garden with Oak, Maple and Birch trees?
Firstly, I would suggest having the old Oak, Maple and Birch trees pruned in order to open up the canopy. This will not only let more light into the garden but will also be healthier for the trees as air will be able to circulate more freely warding off diseases such as black spot and downy mildew.
If grass is truly wanted in the garden, I would suggest a Perennial Ryegrass as a good start as it is good in the shade. This could be mixed with a Tall Fescue which is spread by rhizomes and is quite drought tolerant.
If grass is not essential, I would suggest making some garden beds where perennials such as Hosta would thrive. Also the use of ground covers may be appropriate.
A good landscape designer should be able to help create a harmonious garden using a mix of hard and soft-scaping. Contact Landscape Ontario or ask neighbours, family and friends for recommendations.