I would think asking a specialist strata lawyer would be fairly inevitable so you may as well do that now.
The first thing they are going to ask is whether the “private” garden is part of the lot or common property.
If it’s the latter, then the issue is entirely with the Owners Corporation. If it’s the former, then it’s probably a dispute between two neighbours.
By the way, your neighbour – who will undoubtedly be very annoyed – should probably take the matter up with the original builder who sold a property knowing that they had no rights to some of the area that they were selling.