Ofnhanskarnir hanga við ofninn, svo ég finn þá strax þegar ég tek bökunarplötuna út úr ofninum.

Icelandic makes compound nouns very freely, so ofn + hanskar becomes ofnhanskar.

• ofn = oven
• hanskar = gloves / mitts
• ofnhanskar = oven mitts
• ofnhanskarnir = the oven mitts

The ending -nir is the definite article attached to a masculine plural noun in the nominative case.

Because the subject is plural: Ofnhanskarnir.

The verb hanga means to hang. Its present-tense forms include:

• ég hangi = I hang
• hann/hún/það hangir = he/she/it hangs
• þeir/þær/þau hanga = they hang

So Ofnhanskarnir hanga means the oven mitts hang / are hanging.

This is because different prepositions require different cases.

• við takes the accusative
• úr takes the dative

So the noun ofn changes form:

• ofninn = the oven in the accusative
• ofninum = the oven in the dative

That gives:

• við ofninn = by the oven
• úr ofninum = out of the oven

Here við means something like by, next to, or at.

So hanga við ofninn means the oven mitts are hanging by the oven or next to the oven, not literally inside it.

Because þá is the accusative plural masculine form of the pronoun, and it is the direct object of finn.

It refers back to ofnhanskarnir, which is masculine plural.

Compare:

• þeir = they, nominative
• þá = them, accusative

So:

• þeir hanga = they hang
• ég finn þá = I find them

It is a compound noun plus case ending plus the definite article.

Base noun:

• plata = plate / tray

Compound:

• bökunarplata = baking tray / baking sheet

In the sentence, it is the direct object of tek, so it must be in the accusative singular definite:

• bökunarplata = a baking tray
• bökunarplatan = the baking tray, nominative
• bökunarplötuna = the baking tray, accusative

You may also notice the vowel change a → ö in the oblique form plötu. That is a normal pattern in many Icelandic nouns.

Because út úr is a very common combination meaning out of.

• út = out
• úr = out of / from inside

Together they give the natural idea of movement from inside to outside:

• tek ... út úr ofninum = take ... out of the oven

Also, úr requires the dative, which is why we get ofninum.

The sentence describes a usual or repeated situation, not one single completed event.

So Icelandic uses the present tense:

• ég finn þá strax = I find them right away
• þegar ég tek ... út úr ofninum = when I take ... out of the oven

This is similar to English in sentences about habits or regular actions, especially after when.

Here svo means so or therefore.

It connects the two ideas:

• the oven mitts hang by the oven
• therefore I find them immediately

In other contexts, svo can also mean then, and then, or thus, depending on the sentence.

Strax means immediately or right away.

The order ég finn þá strax is a very natural, neutral Icelandic word order:

• ég = subject
• finn = verb
• þá = object
• strax = adverb

Icelandic word order is somewhat flexible, but this placement sounds normal and idiomatic here.

Þegar means when and introduces a subordinate clause:

• þegar ég tek bökunarplötuna út úr ofninum

A useful grammar point is that after a subordinating conjunction like þegar, Icelandic does not use the main-clause V2 order. So you get:

• þegar ég tek ...

not

• þegar tek ég ...

That makes this clause structure very important to recognize.

Yes. The comma separates two main clauses:

• Ofnhanskarnir hanga við ofninn
• svo ég finn þá strax þegar ég tek bökunarplötuna út úr ofninum

This kind of comma is very common in Icelandic when one full clause is followed by another connected clause.