How to use articles with 'positions'?

Lets's say we have a simple sentence about a fact that always (almost) applies, such as: 'Birds make their nests on the trees'.

There is no article before 'Birds' as it is a generalisation. What about the other nouns? Could we just say: 'Birds make nests on trees', as all the nouns are referred to generally?

Do we always need an article when talking about positions, such as 'Under the bed' or 'On the table'? Or could one get away with saying just 'You should never sleep on tables'?