I think that the strip method, with a little judicious care, can give as 'correct' a solution as a FEM approach. In the y-direction, would consider the slab fixed at the ends of the shear walls and increase the tributary width to reflect this. In addition, at the ends of the walls I would concentrate some of the negative reinforcing at the wall due to the 'knife edge' type of support. In addition, I would put concentrated positive reinforcing in the same area, but to resist/minimise cracking from the high concentration of shear. An FEM model will likely bear the above out. The trickier parts are the torsion in the intersecting beam and the non-colinear walls at the end... but, they can be accommodated in a similar fashion.
Other than that, it looks like a flat slab or sorts... Reinforcing may not be optimal, but, there's a bit of a price to pay for an irregular shaped floor slab.
FEM will give you a bit of an understanding in how the slab will behave and/or deflect, but, it will not necessarily give you a more precise solution... it will show you where you have high degrees of fixity that should be accommodated. With the 'knife edge' conditions, this fixity will drop off a bit as the slab cracks.
My 2c, Dik