1) the engine oil level is low 2) the engine oil is old - making it very thin, especially after the engine warms up. Likely the oil light is doing its job and calling your attention to the level and condition of the engine oil.
if the coolant light is flashing red it means it's overheating (DO NOT DRIVE), check coolent level "if level is fine", it may be your thermastat. if coolent level is low check your coolent hoses. (allow engine to cool before checking)