Vi tog omvägen genom dalen.

Because tog is the past tense of the verb ta (to take).

• ta = infinitive, to take
• tar = present tense, take / are taking
• tog = past tense, took
• tagit = supine/past participle form used in perfect tenses

So:

• Vi tar omvägen = We take / are taking the detour
• Vi tog omvägen = We took the detour

This verb is irregular, so you cannot build the past tense by just adding a regular ending.

Omvägen means the detour or the long way around.

The base noun is:

• en omväg = a detour

The form in the sentence is:

• omvägen = the detour

So the ending -en marks the definite singular form for this en-word noun.

This sentence uses a very natural Swedish expression:

• ta omvägen = take the detour / go the long way around

Because Swedish often adds the definite article to the end of the noun instead of putting a separate word before it.

Compare:

• en omväg = a detour
• omvägen = the detour

This is a very important feature of Swedish grammar. In English, you say the detour with a separate word. In Swedish, the definiteness is built into the noun itself.

Because omvägen is the direct object of the verb tog.

The structure is:

• Vi = subject
• tog = verb
• omvägen = object
• genom dalen = prepositional phrase telling the route

So Swedish works like English here:

• We took the detour
• Vi tog omvägen

You do not need a preposition before omvägen.

Genom dalen means through the valley.

• genom = through
• dalen = the valley

The noun is:

• en dal = a valley
• dalen = the valley

So:

• genom dalen = through the valley

This part tells you where the detour went or what route they took.

Because the sentence refers to the valley, not just a valley.

• en dal = a valley
• dalen = the valley

So:

• genom en dal = through a valley
• genom dalen = through the valley

Swedish uses the definite ending -en here for the same reason English uses the.

Yes, absolutely.

There is a small difference:

• Vi tog omvägen genom dalen = We took the detour through the valley
  This suggests a more specific or known detour.
• Vi tog en omväg genom dalen = We took a detour through the valley
  This sounds less specific and simply states that they took some detour.

So both are grammatical, but the definite form omvägen can make it sound like a particular route is being referred to.

Yes, this is completely normal Swedish word order for a main clause.

The sentence is:

• Vi = subject
• tog = verb
• omvägen = object
• genom dalen = adverbial/prepositional phrase

So the pattern is:

Subject + verb + object + place/path expression

That is a very common Swedish sentence structure.

Yes, it is a very natural expression in Swedish.

• ta en omväg = take a detour
• ta omvägen = take the detour / go the long way around

So this is not a strange literal translation. It is a normal way to talk about choosing a longer route.

Genom is a preposition meaning through.

It is used for movement from one side or part of something to another:

• genom skogen = through the forest
• genom staden = through the city
• genom dalen = through the valley

In this sentence, it describes the path of the detour.

In the present tense, it would be:

• Vi tar omvägen genom dalen.

That means We take the detour through the valley or We’re taking the detour through the valley, depending on context.

Compare:

• Vi tog omvägen genom dalen. = past, We took the detour through the valley
• Vi tar omvägen genom dalen. = present, We take / are taking the detour through the valley