sorry to hear this, as the cooling system is sually good on the mr2 unless its been neglected..
you said there was oil coming from the reservoir over flow??? or was it red coolant you though was oil..
boiling coolant will evaporate as soon as it spews out from the engine so saying on 2 litres was lost is a gamble at best. and if its anything like i had the coolant will just boil out the reservoir and dissapear
the radiator isnt warm because theres no coolant in it , so you have lost more than 2 litres i think
and driving 2kms after finding an overheating problem wasnt the best idea either.
in my case i had an headgasket issue, and coolant was coming out the oveflow tank until it got to a point where there want any coolant left in the block and then the temp. gauge would skyrocket, this was taking about 45 mins to happen, so i wasnt aware of it straight away... there ended up being a small crack in the gasket which would slowly leak and eventually cause overheating in my case..
either way make sure the car is filled PROPERLY with coolant (13.6 litres afaik) and then check for issues, i would replace the thermostat as well to rule that out