Για πρωινό τρώω βρώμη με γιαούρτι όταν δεν θέλω ψωμί.

Για πρωινό literally means for breakfast. Greek often uses για + accusative to show what meal something is for:

• Για πρωινό = for breakfast
• Για μεσημεριανό = for lunch
• Για βραδινό = for dinner

Starting the sentence with Για πρωινό brings breakfast to the front as the topic: as for breakfast, I eat...

Greek often leaves out subject pronouns because the verb ending already shows who the subject is.

• τρώω = I eat
• θέλω = I want

So εγώ is not needed. You would only add εγώ for emphasis or contrast:

• Εγώ τρώω βρώμη... = I eat oats...

The Greek present tense can cover both ideas, depending on context.

• τρώω can mean I eat
• or I am eating

In this sentence, because it describes a usual habit, it means I eat in the sense of I usually eat.

Βρώμη literally means oats. In natural English, depending on context, that might be translated as:

• oats
• oatmeal
• sometimes porridge/oatmeal if that is what is meant

In this sentence, βρώμη με γιαούρτι suggests oats eaten with yogurt, rather than a cooked porridge.

με means with, so:

• βρώμη με γιαούρτι = oats with yogurt

This is a very common structure in Greek: noun + με + noun.

Also, γιαούρτι is in the accusative after με, but for this noun the nominative and accusative look the same, so the form does not change.

Greek often leaves out the article with foods and other mass nouns when speaking in a general, non-specific way.

So:

• τρώω βρώμη = I eat oats / oatmeal
• με γιαούρτι = with yogurt
• δεν θέλω ψωμί = I don't want bread

If you add an article, it usually sounds more specific:

• το γιαούρτι = the yogurt / this yogurt
• το ψωμί = the bread

In this sentence, όταν is best understood as when in the habitual sense, so in English it often feels like whenever.

• όταν δεν θέλω ψωμί = when / whenever I don't want bread

Because the whole sentence describes a repeated habit, whenever is the idea.

δεν is the normal negation word used before verbs in the indicative.

• θέλω = I want
• δεν θέλω = I do not want / I don't want

So όταν δεν θέλω ψωμί means when I don't want bread.

Yes. ψωμί without an article here means bread in a general sense, not a specific loaf or piece.

• δεν θέλω ψωμί = I don't want bread
• δεν θέλω το ψωμί = I don't want the bread

The version in your sentence is the natural one for general food preference.

They are all in the accusative, but in this sentence most of them look the same as the dictionary form.

• Για πρωινό: πρωινό is accusative after για
• τρώω βρώμη: βρώμη is the direct object
• με γιαούρτι: γιαούρτι is accusative after με
• θέλω ψωμί: ψωμί is the direct object of θέλω

This is useful to know even though the forms do not visibly change much here.

Yes. Greek word order is fairly flexible, and changing it usually changes emphasis more than basic meaning.

For example:

• Τρώω βρώμη με γιαούρτι για πρωινό όταν δεν θέλω ψωμί.
• Όταν δεν θέλω ψωμί, για πρωινό τρώω βρώμη με γιαούρτι.

All of these are understandable. The original sentence puts Για πρωινό first, which highlights the breakfast context.