why would any entity invade (which is expensive), but still give back to the people there afterwards if the oil is the only profit from the invasion?

The people needs to rebel, and have a civil war. Take back the country, and rebuild the oil infrastructure. remove price control of goods, and let the market work.

Where has this worked out, historically?

When Vietnam invaded Cambodia and overthrew the Khmer Rouge regime. They did so for pragmatic geopolitical reasons but provided the benefit of dismantling one of the most callous regimes in history.

Scotland, maybe?

This would go exactly as well as it did in Vietnam and Iraq: The Venezuelan people would slaughter the invading imperialists until they gave up and went home.