Devo consegnare il documento oggi stesso.

Because dovere is a modal verb in Italian, and modal verbs are followed directly by the infinitive.

So:

• devo consegnare = I have to deliver / I must hand in

No a or di is used here.

This is similar to:

• voglio mangiare = I want to eat
• posso uscire = I can go out
• devo studiare = I have to study

It can mean both.

In many everyday contexts, devo can be translated as either:

• I must
• I have to

The difference in English is often about tone:

• I must can sound a little stronger or more formal
• I have to is often more common in everyday speech

In Italian, devo covers both ideas very naturally.

Because Italian often drops the subject pronoun when it is already clear from the verb form.

• devo already tells you the subject is I
• so io devo is possible, but usually unnecessary

You would use io only for emphasis, contrast, or clarity:

• Io devo consegnare il documento, non tu.
  I have to hand in the document, not you.

So in a neutral sentence, Devo consegnare... is the most natural choice.

Consegnare means something like:

• to deliver
• to hand in
• to submit
• sometimes to hand over

In this sentence, with il documento, the most natural English ideas are:

• to hand in the document
• to submit the document

It often suggests giving something to the person or office that is expecting it.

Italian uses the definite article much more often than English.

So il documento means:

• the document

Even when English might say I have to hand in my document or just I have to hand in the document, Italian often keeps the article.

Here, il documento usually suggests a specific document that both speaker and listener understand from context.

Oggi stesso adds emphasis to oggi.

• oggi = today
• oggi stesso = today itself / as early as today / today, no later

It suggests urgency or emphasis:

• not tomorrow
• not later
• today

So it is stronger than just oggi.

For example:

• Devo consegnare il documento oggi. = I have to hand in the document today.
• Devo consegnare il documento oggi stesso. = I have to hand in the document today itself / today, no later.

Because in this expression, stesso is used to reinforce the time word.

So:

• oggi stesso = today itself
• domani stesso = tomorrow itself
• ora stessa = right now / this very moment

This placement is normal and idiomatic in Italian.

You would not normally say stesso oggi in this meaning.

No. Stesso has several uses.

It can mean same:

• lo stesso documento = the same document

But in expressions like oggi stesso, it means something more like:

• itself
• this very
• exactly this

So here it is not same, but an emphatic word.

Because the obligation exists now, even if the actual delivery happens later.

Italian often uses the present tense this way:

• Devo studiare stasera. = I have to study tonight.
• Domani parto. = I’m leaving tomorrow.

So devo consegnare il documento oggi stesso means:

• right now, I have the obligation to hand it in today

Yes, a little, but the original sentence is very natural.

Standard order:

• Devo consegnare il documento oggi stesso.

Possible variations:

• Oggi stesso devo consegnare il documento.
  This puts more emphasis on today itself.
• Il documento devo consegnarlo oggi stesso.
  This is more marked and emphatic.

For normal speech, the original version is the safest and most natural.

Yes, but the nuance is a little different.

• oggi stesso = today itself / today, no later, with emphasis
• entro oggi = by today / before the end of today

Both can work, but:

• oggi stesso sounds more emphatic or urgent
• entro oggi sounds a bit more like a deadline formula

So they are similar, but not exactly identical.

It is neutral and works in both formal and informal situations.

Nothing in it is especially casual or especially formal.
It could be said:

• to a friend
• to a coworker
• in an office context
• in everyday conversation

The sentence is simple, standard Italian.