I agree with Poli. The word order makes no difference. A speaker may prefer one or the other, depending on what they have in mind at the moment.
This is not a rule and the speaker may not be conscious of it, but normally if you say first "en Madrid", you prefer to stress the place, and if you say first "(durante/por) dos meses", the time you spent there is more important.
We also take into account how the sentence sounds in our ears, so we choose as we like better.
As for "por" and "durante" being interchangeable... hmm... I'd like to complicate things a little.
1) Let me be a little evil here:
in
the dictionary, "por" is not associated with any notion of time, except an unrelated one, to talk about an approximate date:
– Juan me va a pagar el dinero por junio. -> Juan will pay me back the money by June.
– Creo que la última vez que nos vimos fue por Navidad. -> I think the last time we met it was around Christmas.
But don't worry! You may still say "trabajé en Madrid durante dos meses" and "trabajé en Madrid por dos meses", with exactly the same meaning, and everyone understands. Because of the influence of English, most native speakers will find natural the sentence with "por". In this context, both prepositions are perfectly interchangeable.
2) When you have a verb like "estar", which already expresses some notion of duration, some of us might prefer no preposition:
- Estuve en Madrid dos meses.
You may perfectly say "estuve en Madrid durante dos meses" or "estuve en Madrid por dos meses; it's not wrong at all. Some of us, pedantic ones, would rather omit the preposition.
- Permaneció inmóvil varios minutos.
I'll add a little nuance here: if you don't have a specific unit of time, we will want "durante":
- Estuve allá durante la guerra.
- Estuvimos en casa durante la primavera.
In these cases, we don't use "por", because in that case, the preposition introduces the cause why people have been in some place, rather than the period of time they have been there.
3) Finally, "durante" implies simultaneity. For example, you are in a place while the period of time occurs. So, we'd rather not use "durante" with a verb like "invitar", because you can't invite someone for a loooong period of time; that's an action that happens only once:
- Me invitó a su casa un mes.
- Me invitó a estar (durante/por) un mes en su casa.
- Me invitó a pasar un mes en su casa.
- Me invitó a quedarme (durante/por) un mes en su casa.
I think "me invitó a su casa por un mes" is alright, because the notion of "por" is immediately associated to the time expressed in the sentence rather than the nature of the verb, but I would definitely not use "durante" here for the reason I told before.
