Nincs áram a házban, ezért két gyertyát teszek az asztalra.

Because Hungarian uses nincs as the negative form of van when it means there is / there are.

• van áram = there is electricity / there is power
• nincs áram = there is no electricity / no power

So nem van is not the normal way to say this in modern Hungarian.
In this sentence, Nincs áram means There is no electricity / power is out.

Hungarian often leaves out the article with mass nouns or in very general statements.

So:

• Van áram. = There is electricity / power.
• Nincs áram. = There is no electricity / power.

Adding an article here would sound different or unnatural in this context. The sentence is talking about electricity in general, not a specific the electricity.

A házban means in the house.

It breaks down like this:

• a = the
• ház = house
• -ban / -ben = in

So:

• házban = in the house

Hungarian usually expresses location with a case ending instead of a separate preposition like English in.

Here it is -ban because ház has back vowels, which fits Hungarian vowel harmony.

This is about the two forms of the definite article:

• a
• az

Use:

• a before a consonant sound: a ház
• az before a vowel sound: az asztal

So:

• a házban = in the house
• az asztalra = onto the table

It works a bit like English a/an, except Hungarian uses it for the, not for the indefinite article.

Ezért means therefore, for this reason, or so.

In this sentence, it links cause and result:

• Nincs áram a házban = There is no power in the house
• ezért két gyertyát teszek az asztalra = therefore / so I put two candles on the table

It is a slightly more formal or explicit way to say so.

Because after numbers, Hungarian normally uses the noun in the singular, not the plural.

So:

• egy gyertya = one candle
• két gyertya = two candles
• három gyertya = three candles

Then, because it is the direct object of the verb, Hungarian adds the accusative ending -t:

• két gyertya → két gyertyát

So két gyertyát literally means two candle-ACC, but in natural English it is two candles.

Because gyertyát is in the accusative case, which marks the direct object.

• gyertya = candle
• gyertyát = candle(s) as the thing being put

The verb teszek means I put, so the candles are the direct object, and Hungarian marks that with -t.

The long á appears before the -t because of how this noun forms its accusative:

• gyertya → gyertyát

This is something learners mostly just get used to through exposure.

Teszek is the first person singular present tense form of tesz:

• tesz = to put, place, do

So:

• teszek = I put / I am putting

In this sentence, it means I put.

Hungarian often does not need the subject pronoun, so én is omitted.
Teszek already tells you the subject is I.

This is about the two Hungarian verb conjugations: indefinite and definite.

• teszek = indefinite conjugation
• teszem = definite conjugation

Hungarian uses the definite conjugation when the object is definite and specific, for example:

• A gyertyát teszem az asztalra. = I am putting the candle on the table.

But here the object is két gyertyát = two candles, which is quantified but not definite in the grammatical sense. So Hungarian uses the indefinite form:

• két gyertyát teszek

That is why teszek is correct here.

Because -ra / -re expresses movement onto something.

• asztalra = onto the table
• asztalon = on the table
• asztalban = in the table

Since the action is putting the candles onto the table, Hungarian uses the directional ending -ra.

Compare:

• A gyertyák az asztalon vannak. = The candles are on the table.
  
  • location
• A gyertyákat az asztalra teszem. = I put the candles onto the table.
  
  • movement toward a surface

Hungarian usually drops subject pronouns when the verb already shows who the subject is.

• teszek already means I put
• so én teszek is usually unnecessary

You would add én only for emphasis or contrast, for example:

• Én teszek két gyertyát az asztalra, nem te.
  I’m putting two candles on the table, not you.

So in the original sentence, leaving out én is completely normal.

Hungarian word order is more flexible than English, and it often reflects focus, emphasis, or information structure rather than a fixed subject-verb-object pattern.

This version is a natural, neutral way to say it:

• két gyertyát teszek az asztalra

It presents two candles as the object being put onto the table.

Other word orders are possible, but they can shift emphasis. For example:

• Az asztalra teszek két gyertyát.
  This can put a bit more attention on onto the table.

So the original word order is normal and idiomatic, not strange.

Yes. In normal usage, it can naturally mean either of those in English.

Literally it is:

• There is no electricity in the house

But in context, English speakers would often translate it more idiomatically as:

• The power is out in the house
• There’s no power in the house

So the Hungarian sentence is simple and natural, while English may choose a more idiomatic phrasing depending on context.