Jos minulla on huono olo, pysyn kotona.

Jos means if.

So the sentence has this basic structure:

Jos minulla on huono olo, pysyn kotona.
= If I feel unwell, I stay home.

The jos clause gives the condition, and the second clause gives the result.

Because Finnish often uses minulla on ... for ideas that English expresses with I have ... or sometimes I feel ....

So:

• minä = I
• minulla = literally on me / at me

In this sentence, minulla on huono olo is literally something like there is a bad feeling on me/with me, but naturally it means I feel unwell.

This is a very common Finnish pattern.

Because this is the special minulla on ... structure.

In that structure, Finnish uses olla in the 3rd person form:

• minulla on = I have
• sinulla on = you have
• hänellä on = he/she has

So even though the meaning is about me, the form is still on, not olen.

That is why:

• Minulla on huono olo = correct
• Minulla olen huono olo = not correct

Huono olo is a very common expression meaning feeling unwell, feeling sick, feeling bad, or sometimes feeling nauseous.

Literally:

• huono = bad
• olo = feeling/state/condition

But as a whole, huono olo is best learned as a set phrase.

Depending on context, it can mean:

• physically ill
• nauseous
• generally unwell
• not feeling right

Because Finnish usually does not need the subject pronoun when the verb ending already shows the person.

Here:

• pysyn = I stay / I remain

The ending -n already tells you it is I.

So:

• pysyn kotona = I stay home
• minä pysyn kotona = also possible, but more emphatic

Finnish often leaves out minä, sinä, etc. unless there is some contrast or emphasis.

Pysyn comes from pysyä, which means to stay, to remain, or to keep staying.

So:

• pysyn kotona = I stay at home / remain at home

Compared with some related options:

• olen kotona = I am at home
  This just states location.
• pysyn kotona = I stay at home
  This emphasizes remaining there.
• jään kotiin = I stay home / I remain at home
  This can sound more like a decision not to go somewhere else.

In your sentence, pysyn kotona fits the idea of staying home because of not feeling well.

Because kotona means at home, while kotiin means to home / homeward.

Compare:

• Olen kotona. = I am at home.
• Menen kotiin. = I am going home.
• Pysyn kotona. = I stay at home.

So after pysyn, the sentence needs the location where I stay, not the destination where I go.

Because kotona is the normal, idiomatic way to say at home in Finnish.

• kotona = at home
• kodissa = in the home/house

Kodissa sounds more literal and physical, as if you are talking about being inside the building itself.
Kotona is the usual choice when talking about being home in everyday life.

So pysyn kotona is much more natural than pysyn kodissa.

Finnish often uses the present tense in both parts of this kind of sentence, even when the meaning is future.

So:

• Jos minulla on huono olo, pysyn kotona.

can naturally mean:

• If I feel unwell, I stay home
• If I feel unwell, I’ll stay home

This is normal Finnish usage for general conditions and future-like situations.

Because the sentence begins with a subordinate clause:

• Jos minulla on huono olo = the if clause

Then comes the main clause:

• pysyn kotona

In Finnish, when a subordinate clause comes before the main clause, a comma is used between them.

So the comma here is standard punctuation.

Yes. You can also say:

Pysyn kotona, jos minulla on huono olo.

That still means the same thing.

The difference is mainly in focus:

• Jos minulla on huono olo, pysyn kotona.
  Starts with the condition: If I feel unwell...
• Pysyn kotona, jos minulla on huono olo.
  Starts with the result: I stay home...

Both are correct.