Regarding the potency, it will still be good but keep in mind that the neoprene rubber stopper was already punctured numerous times.
As far as sterility hard to say.
If the oily solution looks clear (normal yellow tint) and free of any particulate then I would not be too concerned although I would prefer using up a vial once punctured.
Regarding multi-dose vials:
Simply put, 4 weeks is the standard threshold that pharmaceutical companies are required to meet in testing. They can’t guarantee sterility beyond that. The 28-day rule is, likewise, an important safety measure. The use of preservative agents in injectable solutions generally doesn’t protect them from bacterial contamination completely. They slow development, not eliminate it. Bacteria can actually grow in these vials just fine, albeit more slowly in comparison to most water-based solutions. Case in point, the most bacteria-laden steroid vial I ever sent to an analytical lab was a vial of oil-based testosterone that had been punctured months earlier but not completely used.