Είμαι τόσο πιεσμένος αυτή την εβδομάδα που δεν κοιμάμαι καλά.

In Greek, πιεσμένος is an adjective/participle meaning pressured, stressed, under pressure, so the natural structure is I am stressed:

• Είμαι πιεσμένος = I am stressed / under pressure

Greek often uses είμαι + adjective where English might also say I’m stressed.
You could also hear other expressions with έχω in Greek, such as:

• Έχω άγχος = I’m anxious / I have stress
• Έχω πολλή πίεση = I’m under a lot of pressure

But in this sentence, είμαι πιεσμένος is completely natural and idiomatic.

Πιεσμένος literally comes from the idea of being pressed or under pressure. In this sentence it means something like:

• stressed
• overloaded
• under pressure
• swamped

So it does not usually mean physically squeezed here; it means emotionally or mentally pressured, often because of work, responsibilities, deadlines, etc.

Because πιεσμένος agrees with the subject in gender, number, and case.

Here the subject is the implied I, and the speaker is understood to be:

• masculine singular → πιεσμένος

Other possible forms would be:

• πιεσμένη = feminine singular
• πιεσμένο = neuter singular
• πιεσμένοι / πιεσμένες = plural

So a woman would say:

• Είμαι τόσο πιεσμένη αυτή την εβδομάδα που δεν κοιμάμαι καλά.

Τόσο ... που means so ... that.

In this sentence:

• τόσο πιεσμένος = so stressed
• που δεν κοιμάμαι καλά = that I’m not sleeping well

So the pattern is:

• τόσο + adjective/adverb + που + result

Examples:

• Είναι τόσο κουρασμένος που κοιμήθηκε αμέσως.
  = He is so tired that he fell asleep immediately.
• Μιλάει τόσο γρήγορα που δεν τον καταλαβαίνω.
  = He speaks so fast that I don’t understand him.

This is a very common structure in Greek.

Αυτή την εβδομάδα means this week.

Greek often uses the demonstrative αυτή together with the article την before a noun:

• αυτή η εβδομάδα = this week (subject form / nominative)
• αυτή την εβδομάδα = this week (object/time expression form / accusative)

In the sentence, this week functions as a time expression, and Greek commonly uses the accusative for expressions of time duration or time reference. That is why you see:

• αυτή την εβδομάδα

not

• αυτή η εβδομάδα

The noun εβδομάδα is feminine singular. In this phrase, it is in the accusative, and for this noun the accusative form happens to look the same as the nominative:

• nominative: η εβδομάδα
• accusative: την εβδομάδα

So the noun itself does not visibly change here, but the article does:

• η → την

The demonstrative also changes form:

• αυτή can appear in both nominative and accusative feminine singular, so here it stays αυτή

That is why the full phrase is:

• αυτή την εβδομάδα

Because Greek, like English, often uses the present tense for a current ongoing situation.

• δεν κοιμάμαι καλά = I’m not sleeping well / I don’t sleep well

Since this week is a period that includes now, the present tense is natural. It describes a condition that is currently happening over these days.

Greek present tense can often translate as either:

• I do not sleep well
• I am not sleeping well

depending on context.

Here the second translation is often the most natural in English.

Because καλά here is an adverb, not an adjective.

It describes how the speaker sleeps:

• κοιμάμαι καλά = I sleep well

Compare:

• καλός = good (adjective, used with nouns)
• καλά = well (adverb, used with verbs)

Examples:

• Είναι καλός άνθρωπος. = He is a good person.
• Μιλάει καλά ελληνικά. = He speaks Greek well.

So with κοιμάμαι, you need the adverb καλά.

Δεν is the standard negation word for many verbs in Greek. It means not.

It normally goes right before the verb:

• δεν κοιμάμαι = I do not sleep / I’m not sleeping

That is why the sentence says:

• που δεν κοιμάμαι καλά

not something like:

• που κοιμάμαι δεν καλά

Greek negation placement is much more fixed than in English.

Κοιμάμαι looks like a middle/passive form because it ends in -μαι, but its meaning here is active in English:

• κοιμάμαι = I sleep

This is very common in Greek. Some verbs have middle/passive morphology but are translated actively in English.

Other examples:

• θυμάμαι = I remember
• φοβάμαι = I am afraid / I fear
• έρχομαι = I come

So you should learn κοιμάμαι as the normal verb to sleep, even though its form may look unusual at first.

Yes, Greek word order is fairly flexible, although the original order sounds very natural.

Original:

• Είμαι τόσο πιεσμένος αυτή την εβδομάδα που δεν κοιμάμαι καλά.

You may also hear:

• Αυτή την εβδομάδα είμαι τόσο πιεσμένος που δεν κοιμάμαι καλά.

This version puts more emphasis on this week.

However, the τόσο ... που connection should stay clear, and δεν still stays before the verb.

It sounds very natural in everyday Greek. It expresses a fairly common idea: someone is so stressed this week that it is affecting their sleep.

The tone is:

• natural
• conversational
• slightly emphatic because of τόσο ... που

If you wanted something milder, you might say:

• Είμαι αρκετά πιεσμένος αυτή την εβδομάδα.
  = I’m quite stressed this week.

If you wanted something stronger:

• Είμαι υπερβολικά πιεσμένος αυτή την εβδομάδα.
  = I’m extremely stressed this week.

A few useful points:

• Είμαι is pronounced roughly EE-me
• τόσο has the stress on the first syllable: TO-so
• πιεσμένος has stress on the last syllable: pie-sme-NOS
• εβδομάδα has stress on -μά-: evdo-MA-da
• κοιμάμαι has stress on -μά-: ki-MA-me
• καλά has stress on the second syllable: ka-LA

Stress matters in Greek, so it is worth noticing where the accent marks are.