Po obiedzie myję talerze w zlewie.

Because Polish often drops subject pronouns when they are obvious from the verb form.

Here, myję already means I wash / I am washing, so ja is not necessary.
If you add ja, it usually gives extra emphasis, like I wash the plates, not someone else.

Because the preposition po in the sense of after takes the locative case.

The base noun is obiad.
In the locative singular, it becomes obiedzie.

So:

• obiad = lunch / dinner
• po obiedzie = after lunch / after dinner

This is a very common pattern to memorize: po + locative.

Obiad is the main cooked meal of the day in Polish culture. Depending on context, English may translate it as lunch or dinner.

So po obiedzie could be understood as:

• after lunch
• after dinner

The best translation depends on the situation and the speaker’s routine.

Myję is the 1st person singular present tense of the verb myć (to wash).

So:

• myć = to wash
• myję = I wash / I am washing

The ending -ę is the clue that the subject is I.

It can mean both.

Polish present tense often covers both the English:

• simple present: I wash
• present continuous: I am washing

So myję talerze can mean either:

• I wash the plates
• I am washing the plates

Context tells you which is intended.

Not in the same way.

• myję comes from myć, an imperfective verb
• umyję comes from umyć, a perfective verb

The difference is about aspect:

• myć / myję focuses on the process, habit, or ongoing action
• umyć / umyję focuses on completion

So:

• Po obiedzie myję talerze = After lunch/dinner, I wash / am washing the plates
• Po obiedzie umyję talerze = After lunch/dinner, I will wash the plates / I’ll get the plates washed

A perfective form like umyję does not normally mean a present ongoing action.

Because talerze is the accusative plural form used for the direct object of the verb.

The dictionary form is talerz (plate).
Plural nominative: talerze
Plural accusative: also talerze

For many masculine inanimate nouns in Polish, the accusative plural looks the same as the nominative plural.

So:

• talerze = plates
• myję talerze = I wash the plates / plates

Because w means in, and when it shows location, it takes the locative case.

The noun is zlew (sink).
In the locative singular, it becomes zlewie.

So:

• zlew = sink
• w zlewie = in the sink

A useful contrast:

• w zlewie = in the sink, located there
• do zlewu = into the sink, movement toward it

Because Polish has no articles like English a / an / the.

That means talerze can mean:

• plates
• the plates

And w zlewie can mean:

• in a sink
• in the sink

The exact meaning comes from context, not from an article.

Yes. Polish word order is more flexible than English.

The sentence Po obiedzie myję talerze w zlewie is a natural, neutral order:

• time first: Po obiedzie
• verb: myję
• object: talerze
• place: w zlewie

But other orders are possible, for example:

• Myję talerze w zlewie po obiedzie
• Talerze myję po obiedzie
• W zlewie myję talerze po obiedzie

These versions may sound more marked or emphasize different parts of the sentence. The basic meaning stays similar.

You can work it out from the grammar of the sentence:

• po obiedzie → locative, because po = after takes locative here
• talerze → accusative, because it is the direct object of myję
• w zlewie → locative, because w for location takes locative

So the sentence contains:

• obiedzie = locative singular
• talerze = accusative plural
• zlewie = locative singular

This is a good example of how Polish case endings show the role of each word in the sentence.