Om det kliar i näsan, går jag in och tvättar ansiktet.

Om introduces a condition, just like if in English.

So Om det kliar i näsan, ... means If it itches in my/the nose, ...

A useful thing to remember is that om can also mean about in other contexts, but here it is clearly the conditional if.

Here det is a dummy subject, similar to English it in it hurts, it rains, or it itches.

Swedish often uses det in expressions about:

• weather: Det regnar
• time/general situation: Det är sent
• bodily sensations: Det kliar, Det gör ont

So det kliar i näsan is literally something like it itches in the nose.

They are related, but they do not mean the same thing.

• det kliar = it itches
• jag kliar mig = I scratch myself

This is important because English separates itch and scratch, while Swedish uses the verb klia in closely related ways.

Examples:

• Det kliar i armen = it itches in my arm
• Jag kliar mig på armen = I scratch my arm

So in your sentence, kliar describes the feeling, not the action of scratching.

I is used because the sensation is understood as being in the nose, not just on its outer surface.

• i näsan = in the nose
• på näsan = on the nose

With bodily sensations, Swedish often uses i when something is felt internally or in a body area:

• Det gör ont i ryggen
• Det kliar i ögat
• Det sticker i halsen

So i näsan is the natural choice here.

Because Swedish very often uses the definite form for body parts when it is already obvious whose body part is meant.

So instead of saying:

• min näsa
• mitt ansikte

Swedish often prefers:

• näsan
• ansiktet

This is especially common when the owner is clearly the subject of the sentence.

So:

• tvättar ansiktet is more natural than tvättar mitt ansikte
• i näsan is more natural than i min näsa

Using min/mitt is still possible, but it can sound more emphatic or contrastive.

They are:

• näsan → näsa
• ansiktet → ansikte

The forms in the sentence are the singular definite forms:

• näsa → näsan = the nose
• ansikte → ansiktet = the face

This is helpful because Swedish often attaches the definite article as an ending instead of using a separate word like the.

This is because Swedish follows the V2 rule in main clauses: the finite verb usually comes in the second position.

The first part, Om det kliar i näsan, is a subordinate clause placed first. When that whole clause comes first, the main clause still must put the verb second:

• Om det kliar i näsan, går jag in och tvättar ansiktet.

Not:

• Om det kliar i näsan, jag går in ...

This kind of inversion is very common in Swedish:

• När jag kommer hem, äter jag.
• Om det regnar, stannar vi inne.
• I dag går hon till jobbet.

Går in is the particle verb gå in, which usually means go in or go inside.

So here it means that the speaker goes indoors or goes into a room/building before washing their face.

This is a common Swedish particle verb, similar to English phrasal verbs:

• gå in = go in
• gå ut = go out
• komma in = come in
• ta av = take off

Because gå in is a particle verb, and in Swedish the particle often gets separated when the finite verb moves into second position.

Compare:

• att gå in = to go in
• jag går in = I go in
• om jag går in = if I go in
• går jag in = do I go in / I go in after fronting

So går is the finite verb, and because of Swedish word order it appears earlier, while in stays later.

Because Swedish often uses the present tense for:

• general truths
• habits
• repeated reactions
• near-future meaning in conditionals

This sentence sounds like a general reaction or routine:

• If my nose itches, I go in and wash my face.

It does not have to mean that this is happening right now. It can mean whenever this happens, that is what I do.

This is very normal in Swedish conditionals.

Because both verbs have the same subject, so Swedish can coordinate them with och without repeating the subject.

• går jag in och tvättar ansiktet

This means:

• I go in and wash my face

Repeating jag would usually be unnecessary here.

You can think of it as:

• går jag in
  • [jag] tvättar ansiktet

The second jag is simply left out because it is understood.