“Gaal.” Related to “to abhor, to loathe.” This would not have been his birth-name, but a name he earned by how he lived.

“Ebed.” Ebed means “servant, slave.” Thus Gaal son of Ebed can mean something like “Loathsome, son of a slave.”

“with his brothers.” This use of “brothers” means relatives, extended family.

“moved into Shechem.” Or, they “crossed through” Shechem, but the fact that they are there for a while seems to indicate they moved in, even if just temporarily (cp. ESV).