Μετά τη συνομιλία μας ένιωσα πιο καλά.

Because μετά as a preposition normally takes the accusative case in Modern Greek.

• η συνομιλία = nominative, the conversation
• τη συνομιλία = accusative, the conversation after a preposition like μετά

So:

• μετά τη συνομιλία = after the conversation

Also note that μετά can be an adverb in other contexts, meaning something like afterwards or later, but here it is clearly a preposition followed by a noun phrase.

Τη is just the shorter form of την.

In Modern Greek, the final -ν of τον / την is often dropped before many consonants. Since συνομιλία begins with σ, it is very normal to say:

• τη συνομιλία

rather than:

• την συνομιλία

Both may be understood, but τη συνομιλία sounds more natural in standard everyday usage.

Συνομιλία is a feminine noun meaning conversation, chat, or talk.

Its basic forms are:

• η συνομιλία = the conversation
• της συνομιλίας = of the conversation
• τη συνομιλία = the conversation (object / after a preposition)

In this sentence it is in the accusative because of μετά.

In Greek, weak possessive forms like μου, σου, μας, σας, τους usually come after the noun.

So Greek says:

• η συνομιλία μας = our conversation

not usually a direct equivalent of English our conversation with our in front.

This is very common in Greek:

• το σπίτι μου = my house
• ο φίλος σου = your friend
• η ιδέα μας = our idea

So τη συνομιλία μας is the normal way to say our conversation.

Ένιωσα is the aorist of νιώθω or αισθάνομαι-type meaning to feel.

Here it means I felt as a single completed event in the past.

Compare:

• ένιωσα = I felt
• ένιωθα = I was feeling / I used to feel

So in this sentence, ένιωσα presents the feeling as something that happened after the conversation, as one complete past experience.

Because Greek often drops subject pronouns when they are already clear from the verb ending.

The ending of ένιωσα already tells you the subject is I.

So Greek does not need εγώ unless you want emphasis or contrast:

• ένιωσα πιο καλά = I felt better
• εγώ ένιωσα πιο καλά = I felt better

That second version sounds more emphatic, as if contrasting with someone else.

Yes, καλύτερα would also be possible.

Both of these can mean better:

• πιο καλά
• καλύτερα

In everyday Greek, πιο καλά is very common and natural. Καλύτερα is also very common and may sound a bit more compact or slightly more standard depending on context.

So these are both fine:

• Ένιωσα πιο καλά.
• Ένιωσα καλύτερα.

In this sentence, πιο καλά is perfectly normal.

Yes, καλά is formally the adverb form, but with verbs like νιώθω it is very natural Greek.

Greek commonly says:

• νιώθω καλά = I feel well / I feel good

Even though English often prefers good after feel, Greek normally uses καλά in this type of expression.

So:

• ένιωσα πιο καλά literally uses the adverb form, but idiomatically it is exactly what Greek speakers say.

This is one of those places where Greek and English do not match word-for-word.

Yes. Greek word order is fairly flexible.

Your sentence:

• Μετά τη συνομιλία μας ένιωσα πιο καλά.

is completely natural. But you could also say:

• Ένιωσα πιο καλά μετά τη συνομιλία μας.

Both mean the same thing. The difference is mostly about focus and rhythm:

• starting with Μετά τη συνομιλία μας puts the time/context first
• starting with Ένιωσα puts the action first

Greek often moves parts of the sentence around more freely than English does.

Yes. If you want to strengthen the comparison, you can say:

• ένιωσα πολύ πιο καλά = I felt much better

You could also hear:

• ένιωσα πολύ καλύτερα

Both are natural. Greek often uses πολύ to mean much in comparisons like this.

Other words are possible, but they are not always exactly the same.

For example:

• συνομιλία = conversation, talk
• συζήτηση = discussion, conversation
• κουβέντα = chat, talk, often a bit more informal

So you might also hear:

• Μετά τη συζήτησή μας ένιωσα πιο καλά.
• Μετά την κουβέντα μας ένιωσα πιο καλά.

These are similar, but συνομιλία is a good neutral choice.

Because Greek usually keeps the definite article with possessed nouns.

English says:

• our conversation

but Greek normally says:

• η συνομιλία μας
• τη συνομιλία μας in the accusative

This is very normal Greek structure. In other words, Greek often uses:

article + noun + possessive

rather than just possessive + noun as English does.