Været er elendig.

Været is the definite singular form of vær.

• vær = weather
• været = the weather

So the sentence is literally The weather is awful.

In Norwegian, it is very normal to use the definite form when talking about the current weather in a general way.

It is built into the noun.

Norwegian often puts the definite article at the end of the noun instead of using a separate word in front:

• et hus = a house
• huset = the house

The same thing happens here:

• vær = weather
• vær-et = the weather

So været already includes the meaning of the.

Vær is a neuter noun.

That matters because neuter nouns use:

• et in the indefinite singular: et vær
• -et in the definite singular: været

It can also affect adjective forms in some situations, for example:

• et stort hus = a big house
• huset er stort = the house is big

With vær, you get:

• et elendig vær
• været er elendig

Because adjectives ending in -ig usually do not add -t in the neuter singular.

Many Norwegian adjectives change form with gender and number, but elendig belongs to a group that stays the same in singular common gender and neuter:

• en elendig dag = a terrible day
• et elendig vær = terrible weather
• været er elendig = the weather is terrible

In the plural or in definite adjective forms, you normally get elendige:

• elendige forhold = terrible conditions

Er is the present tense of å være, which means to be.

It works like English is / am / are, but Norwegian uses the same form for all persons:

• jeg er = I am
• du er = you are
• han er = he is
• vi er = we are

So in Været er elendig, er simply means is.

Yes. This is the basic order for a simple statement:

• Været = subject
• er = verb
• elendig = predicative adjective

So it is subject + verb + complement, just like English The weather is awful.

A useful extra point: Norwegian main clauses follow the verb-second rule. That means if you move something else to the front, the verb still stays in second position:

• I dag er været elendig. = Today the weather is awful.

A rough guide:

• været ≈ VAIR-eh or VAIR-uh
• elendig ≈ eh-LEN-di

A few helpful details:

• æ is a front vowel somewhat like the vowel in cat or bad, though exact pronunciation varies.
• In været, the final -et is often reduced in speech.
• In elendig, the stress is on the middle syllable: e-LEN-dig.
• In many spoken varieties, final -ig sounds more like -i than a strong English g.

As always with Norwegian, pronunciation varies a lot by dialect.

Yes. That is also very natural.

Both are correct, but they are built differently:

• Været er elendig. = The weather is awful.
• Det er elendig vær. = It is awful weather.

The second sentence uses det as a dummy subject, similar to English it in weather expressions.

Very roughly:

• Været er elendig sounds like you are commenting on the weather as the topic.
• Det er elendig vær sounds like a general description of the conditions.

In everyday speech, you will hear both.

Yes. Elendig is usually stronger and more emphatic than dårlig.

• dårlig = bad / poor
• elendig = awful / terrible / lousy

So Været er elendig sounds quite negative. It is not just mildly bad weather; it sounds really unpleasant.

For comparison:

• Været er dårlig. = The weather is bad.
• Været er elendig. = The weather is awful.