Neither of these are exact equivalents of simply 'stay up late'. We wouldn't use them just to say that you went to bed later than usual because you were watching TV or chatting with friends. Both mean that you are WORKING late at night - studying, reading, writing or getting other work done. The first is an old expression, dating back to before the invention of the electric light bulb, but it is still sometimes used today. A related expression is 'burning the candle at both ends', meaning that you go to bed late and get up early. 'Pull an all-nighter' is modern expression, and it's much more informal. As you'd expect, it means not going to bed at all. If you pull an all-nighter, you work right through the night.

I personally think that "to burn the midnight oil" is pretty old-fashioned. I can't remember the last time I heard somebody my age say it. Most people my age say "to pull an all-nighter" or "to stay up all night". The other common expression that comes to mind is "to be a night owl", which usually refers to somebody that gets up late and goes to bed late. Laurence

I am a native English speaker and I live in the Mid-Western U.S. "Burn the midnight oil" is outdated. "Pull an all nighter" is used, but it means to not sleep for the entire night. Honestly, we just say "stay up late", although there might be an idiom from another country that I don't know.

what idioms are commonly used to say "stay up late"？i am learning English grammar these days, and i want to know whether it right or not？:)