There are reasons to avoid it that go beyond performance, and the first one is likely to settle it.
It may well be illegal where you are. Used engine oil is classified as hazardous waste in many jurisdictions. It must be collected and taken to a proper disposal point, and applying it to timber that will sit outdoors in the weather is disposal by another name. Rules vary and it is worth ten minutes checking yours, because "the builder suggested it" is not a defence.
It is a genuine contaminant. Used oil is not fresh oil. It contains combustion products, metals worn from the engine, and additives that have degraded. Applied to timber outdoors it will leach into the ground with every rainfall, and it will do so for years.
For a bin enclosure at a beach house — near sand, near drainage, near water — that is the part I would weigh most heavily.