Hun har stor innflytelse.

Because Norwegian uses ha (to have) in this expression, just like English says she has influence.

• Hun har stor innflytelse = She has great influence
• Using er would mean is, which does not fit here.

So this is a normal pattern:

• ha innflytelse = to have influence

Stor literally means big or large, but with abstract nouns it often means great, strong, or significant.

So stor innflytelse means:

• great influence
• a lot of influence
• significant influence

It sounds natural in Norwegian.

Because innflytelse is being used as an abstract, uncountable idea here.

In English, we often also say:

• She has influence
• She has great influence

Norwegian works similarly in many cases with abstract nouns:

• Hun har erfaring = She has experience
• Han har makt = He has power
• Hun har stor innflytelse = She has great influence

You could sometimes use an article in other contexts, but in this sentence it is very natural without one.

The adjective must match the noun.

Innflytelse is a common-gender noun:

• en innflytelse

For a singular en-word, the adjective usually takes the basic form:

• stor innflytelse

Compare:

• en stor bil
• et stort hus
• store biler

So:

• stor = singular common gender
• stort = singular neuter
• store = plural or definite forms

It is usually an en word:

• en innflytelse

That is why the adjective form is stor.

Example:

• en stor innflytelse = a great influence

In your sentence, the article is simply left out.

Yes, absolutely.

Both are natural, but they are slightly different in tone:

• Hun har mye innflytelse = She has a lot of influence
• Hun har stor innflytelse = She has great/significant influence

Mye focuses more on quantity, while stor often sounds a bit more formal or emphasizes importance.

The sentence follows the normal Norwegian main-clause pattern:

• Hun = subject
• har = verb
• stor innflytelse = object/complement

So:

• Hun har stor innflytelse.
• Subject + verb + rest

This is the same basic order as in English:

• She has great influence.

A rough guide is:

inn-fly-tehl-se

A few useful points:

• inn sounds like in with an extra n
• fly sounds somewhat like flew, but with the Norwegian y sound, which is different from English
• the stress is usually on the first syllable: INN-flytelse

If pronunciation is your focus, the hardest part is often the y in fly.

Yes, it sounds completely natural.

It works in both everyday and more formal contexts. Depending on context, Norwegian speakers might also say:

• Hun har mye innflytelse
• Hun er innflytelsesrik = She is influential

But your sentence is correct and idiomatic.

Yes. That means She is influential.

The difference is:

• Hun har stor innflytelse = focuses on the influence she has
• Hun er innflytelsesrik = describes her as an influential person

Both are correct, but innflytelsesrik is an adjective, while har stor innflytelse uses a noun phrase.

Hun is the subject pronoun meaning she.

Examples:

• Hun kommer = She is coming
• Hun har stor innflytelse = She has great influence

It is used for a female person, just like she in English.