Yeah, sure you can eat them. Looks like you have a white-fruited variety of white mulberry? You don't see many of those in New Jersey,most are red-fruited "whites" or are probable red-fruited hybrids with red mulberry.

I have eaten some...they are so sweet! No wonder the birds flock to the tree. Thanks atlamol.

Consider yourself lucky, the white varieties, while invasive, are so much sweeter than our native red/black ones. Just don't eat them before they are absolutely ripe there have been mean reports of people having slightly hallucinogenic, and not the good kind, effect from eating too many un-ripened berries.