Σου χρωστάω δέκα ευρώ.

Σου is the weak form of the personal pronoun meaning to you (singular), used in the indirect object position.

So in Σου χρωστάω δέκα ευρώ, σου means to you:

• σου = to you
• χρωστάω = I owe
• δέκα ευρώ = ten euros

Greek very often uses these short pronoun forms instead of a fuller phrase like σε εσένα.
You could say Σου χρωστάω in normal speech, while Σε εσένα χρωστάω would sound more emphatic, like It’s you I owe.

Yes. Χρωστάω is a common 1st person singular present tense form meaning I owe.

The verb is χρωστάω / χρωστώ, and both forms are used. In modern everyday Greek, χρωστάω is very common.

Some present-tense forms:

• χρωστάω = I owe
• χρωστάς = you owe
• χρωστάει / χρωστά = he/she/it owes
• χρωστάμε = we owe
• χρωστάτε = you (plural) owe
• χρωστάνε / χρωστούν = they owe

So this sentence is literally built around I owe.

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

In χρωστάω, the ending tells you the subject is I, so εγώ is usually unnecessary.

• Χρωστάω δέκα ευρώ = I owe ten euros
• Εγώ χρωστάω δέκα ευρώ = I owe ten euros

Adding εγώ usually gives emphasis, contrast, or clarification.

In Greek, these short object pronouns like μου, σου, του, της, μας, σας, τους usually come before the verb.

So:

• Σου χρωστάω = I owe you
• Μου χρωστάς = you owe me

This is one of the most important word-order patterns to get used to in Greek.
With this type of pronoun, English and Greek are different:

• English: I owe you
• Greek: To-you I-owe

Even though that is the literal structure, the natural English meaning is still just I owe you.

Yes, Greek word order is fairly flexible, but not all versions sound equally neutral.

The most natural neutral order here is:

• Σου χρωστάω δέκα ευρώ.

You may also hear:

• Χρωστάω δέκα ευρώ σε σένα.
  This uses a full prepositional phrase instead of σου.
• Δέκα ευρώ σου χρωστάω.
  This sounds more emphatic, like It’s ten euros I owe you.
• Σου χρωστάω εγώ δέκα ευρώ.
  This can emphasize I.

So yes, the order can shift, but the original sentence is the most straightforward everyday version.

Σου is singular: to you when speaking to one person.

If you are speaking to more than one person, Greek uses:

• σας = to you (plural)

So:

• Σου χρωστάω δέκα ευρώ. = I owe you (one person) ten euros.
• Σας χρωστάω δέκα ευρώ. = I owe you (more than one person, or formal singular in many contexts) ten euros.

Note that σας is also used as a polite/formal singular in many situations.

Because ευρώ is normally indeclinable in modern Greek in everyday use. That means it usually stays the same after numbers.

So you say:

• ένα ευρώ = one euro
• δύο ευρώ = two euros
• δέκα ευρώ = ten euros

Unlike some Greek nouns, ευρώ usually does not change form here.

A simple learner-friendly pronunciation guide would be:

soo hro-STAH-o THEH-ka ev-RO

A few details:

• σου sounds like soo
• χρ in χρωστάω can be tricky; χ is a throaty sound, not an English h
• ωστά carries the stress in χρωστάω
• δ in modern Greek sounds like th in this, so δέκα is closer to THEH-ka
• ευ in ευρώ is usually pronounced ev before a voiced sound like ρ

So:

• χρωστάω ≈ hro-STAH-o / khro-STAH-o
• ευρώ ≈ ev-RO

It is in the present tense, but in this case the present has a meaning similar to English I owe.

Greek present tense can describe a current state or situation, and owing money is treated as a present state:

• Σου χρωστάω δέκα ευρώ. = I owe you ten euros.

It does not mean I am owing you ten euros in a progressive sense. English simply uses I owe you.

Yes, that is grammatically possible.

Using σε σένα gives the fuller version of to you:

• Χρωστάω σε σένα δέκα ευρώ.

This is more explicit and can sound more emphatic than σου. In normal everyday speech, though, σου is usually the more natural choice unless you want contrast:

• Χρωστάω σε σένα, όχι σε αυτόν. = I owe you, not him.

So both are correct, but σου is the usual unstressed form.

No. Χρωστάω can be used both literally and more broadly.

Literal:

• Σου χρωστάω δέκα ευρώ. = I owe you ten euros.

More general:

• Σου χρωστάω μια απάντηση. = I owe you an answer.
• Του χρωστάω πολλά. = I owe him a lot.

It can refer to money, favors, explanations, gratitude, and other kinds of obligations.

You make it negative with δεν before the verb phrase:

• Δεν σου χρωστάω δέκα ευρώ. = I don’t owe you ten euros.

The order is:

• Δεν
  • pronoun
    • verb

So:

• Δεν σου χρωστάω. = I don’t owe you.
• Δεν μου χρωστάς τίποτα. = You don’t owe me anything.

Both can mean I owe, but they are not used in exactly the same way.

• χρωστάω is very common in everyday spoken Greek
• οφείλω is often more formal, more written, or sometimes used in a broader sense of I am obliged to

Examples:

• Σου χρωστάω δέκα ευρώ. = everyday, natural
• Σας οφείλω μια εξήγηση. = more formal, I owe you an explanation

If you are learning everyday conversation, χρωστάω is the one you will probably hear and use more often.

Yes, in normal written Greek you should include the accent marks.

They help show which syllable is stressed:

• χρωστάω
• δέκα
• ευρώ

Greek spelling normally requires these accents, so learners should get used to writing them. They are not optional in standard writing.