Before you ditch the oil heating, get a proper energy consultant to come to your house - not just the tradespeople who want to sell you a heat pump. That's the crucial point a lot of people miss. A house from '78 can actually work with a heat pump, but the efficiency really depends on how your heating surfaces are sized. If you still have old radiators that are designed for 70 - 80°C, you'll either need a very large heat pump (expensive, bad for electricity consumption) or you'll have to switch to underfloor heating. An energy consultant will look at it properly and tell you whether renovation makes sense first.
On the costs: A heat pump alone runs between 15,000 and 30,000 euros net depending on the type (air, ground source), then you've got disposal of the oil heating, possibly a new buffer tank, electrical upgrades on top of that. If you insulate first - roof, top floor ceiling, maybe basement walls - you'll cut your electricity consumption dramatically later. That pays off in the long run. Here's the thing though: A lot of people put in the heat pump and save less than they hoped for because the building envelope is just too poor.
There are subsidy programs from the government, but the conditions are very specific - the energy consultant should look into that too before you sign anything.