Jag vill gärna ha lagom starkt kaffe efter mötet.

Because vill means want and ha means have. Together, vill ha works like English want to have or, more naturally, want in this context.

So:

• Jag vill ha kaffe = I want coffee
• literally: I want have coffee

This is a very common Swedish pattern:

• Jag vill äta = I want to eat
• Jag vill köpa = I want to buy
• Jag vill ha = I want to have / I want

With ha, Swedish often expresses wanting something in a very direct, everyday way.

Gärna is a very common Swedish adverb. It often adds the sense of gladly, preferably, or would like to.

In this sentence, it softens Jag vill ha and makes it sound more natural and polite:

• Jag vill ha kaffe = I want coffee
• Jag vill gärna ha kaffe = I’d like coffee / I would gladly have coffee

So gärna does not completely change the meaning, but it adds a friendly, less blunt tone.

That is the normal word order in Swedish main clauses. The finite verb usually comes early, and adverbs like gärna often come right after it.

So:

• Jag vill gärna ha ...

is the natural structure.

Compare:

• Jag kan gärna hjälpa dig = I’d be happy to help you
• Hon vill gärna komma = She would like to come

If you move things around, the sentence may sound marked or unnatural unless there is a special reason.

Lagom is a very Swedish word and is often hard to translate with just one English word. It means something like:

• just right
• moderately
• not too much, not too little

In lagom starkt kaffe, it means coffee that is strong enough, but not too strong.

So the phrase suggests a balanced strength. This is one of the most common uses of lagom in Swedish.

Examples:

• lagom varmt = pleasantly warm / just warm enough
• lagom dyrt = reasonably priced
• lagom mycket = just the right amount

Because kaffe is a neuter noun in Swedish: ett kaffe.

When an adjective comes before a singular neuter noun in the indefinite form, it usually takes -t.

So:

• en stark dryck = a strong drink
• ett starkt kaffe = a strong coffee

Here, lagom does not change, but stark becomes starkt to agree with kaffe.

This is standard adjective agreement in Swedish.

Because kaffe is often used as a mass noun, like coffee in English.

So Swedish can simply say:

• Jag vill ha kaffe = I want coffee

without en or ett.

If you say ett kaffe, it often means a coffee in the sense of a cup/serving of coffee, especially when ordering in a café.

So there is a difference:

• Jag vill ha kaffe = I want coffee
• Jag vill ha ett kaffe = I want a coffee

Both are possible, but the version without an article is very natural here.

Mötet is the definite form and means the meeting.

• ett möte = a meeting
• mötet = the meeting

In the sentence, the speaker means a specific meeting that is already known from the context, so Swedish uses the definite form:

• efter mötet = after the meeting

If it were not a specific meeting, you might say:

• efter ett möte = after a meeting

Yes. Swedish allows some flexibility with time expressions and other adverbials.

The original sentence:

• Jag vill gärna ha lagom starkt kaffe efter mötet.

You can also front efter mötet:

• Efter mötet vill jag gärna ha lagom starkt kaffe.

This is also correct. Notice that when Efter mötet comes first, Swedish keeps the verb in second position, so vill comes before jag:

• Efter mötet vill jag ...
• not Efter mötet jag vill ...

That verb-second pattern is very important in Swedish main clauses.

It sounds natural and fairly polite, especially because of gärna.

Still, Swedish has softer alternatives if you want to sound more tentative or extra polite:

• Jag skulle gärna vilja ha lagom starkt kaffe efter mötet.
• Jag skulle vilja ha lagom starkt kaffe efter mötet.

These are closer to I would like to have...

In everyday speech, though, Jag vill gärna ha ... is perfectly normal and not rude by itself. Context matters: saying it to a friend, colleague, or in casual planning sounds fine.

Not exactly a fixed phrase, but it is a very natural combination.

It is built regularly:

• lagom = just right / moderately
• starkt = strong
• kaffe = coffee

So the phrase literally describes coffee of the right strength.

You can make similar phrases:

• lagom varmt te = tea that is just warm enough
• lagom sött kaffe = coffee that is just sweet enough
• lagom kallt vatten = water that is nicely cool

So it is productive, not an idiom you simply have to memorize as one block.