Yes — strawberries are vitamin-rich and loved by almost every parrot. Just wash them very well.
What it means for African greys
There's nothing specific to a african grey that changes the verdict on strawberries — it's treated the same as for parrots generally. Greys can take a larger portion than small parrots.
The full picture on strawberries
Strawberries offer vitamin C, manganese, and folate, and their seeds and leafy tops are harmless. The only real concern is agricultural: strawberries consistently rank among the most pesticide-laden crops, so washing matters more here than for most fruit.
Wash thoroughly or buy organic; the tops are safe to leave on.
Halve or quarter for small species.
A messy fruit — schedule it before cage-cleaning day.