Learn Hardcore Finnish: Minä otan laukun sohvan vierestä. - I take the bag from next to the couch.

Minä otan laukkua. – I’m (in the process of) taking some of the bag / am engaged in taking a bag (incomplete, ongoing, or not total; often sounds odd with bag, but works with things like food, drink, etc.).

So here laukun (genitive) indicates a complete action affecting the whole bag.

Why is it sohvan and not sohva?

Sohvan is also in the genitive case. Many postpositions in Finnish (words like vieressä, vierestä, takana, alta) require the noun before them to be in the genitive.

Pattern:

sohva (sofa) – basic form
sohvan vieressä – next to the sofa (location)
sohvan vierestä – from next to the sofa (movement from)
sohvan viereen – to next to the sofa (movement to)

So the construction is:
[genitive noun] + [postposition]
→ sohvan vierestä.

What exactly does vierestä mean, and how is it different from vieressä and viereen?

All three come from vieri / vieri- meaning something like side / beside / next to, but they use different cases, which change the meaning:

vieressä – inessive case (where?)
- sohvan vieressä – next to the sofa (static location)
viereen – illative case (to where?)
- sohvan viereen – (to) next to the sofa (movement to that position)
vierestä – elative case (from where?)
- sohvan vierestä – from next to the sofa (movement from that position)

So in your sentence:

Minä otan laukun sohvan vierestä.
→ I take the bag from next to the sofa (movement away from that spot).

Can you break the whole sentence down word by word?

Yes:

Minä – I (1st person singular pronoun)
otan – I take (present tense, 1st person singular of ottaa)
laukun – the bag / a particular bag (genitive singular of laukku, total object)
sohvan – the sofa’s / of the sofa (genitive singular of sohva, required before the postposition)
vierestä – from next to / from beside (elative form of vieri, used as a postposition)

Altogether: I take the bag from next to the sofa.

Could I change the word order, for example say Otan sohvan vierestä laukun?

You can change the word order in Finnish more freely than in English, but it affects emphasis and naturalness.

Most neutral here is:

(Minä) otan laukun sohvan vierestä.

Other possibilities:

Laukun otan sohvan vierestä.
→ Emphasis on laukun: As for the bag, I’m taking it from next to the sofa (not somewhere else).
Sohvan vierestä otan laukun.
→ Emphasis on sohvan vierestä: From next to the sofa is where I take the bag (not from somewhere else).
Otan sohvan vierestä laukun.
→ Understandable, but less natural; it can sound a bit clumsy. Usually object comes directly after the verb in a neutral sentence.

So yes, you can move parts for emphasis, but the original order is the most natural everyday choice.

Why is the object laukun in genitive and not in partitive (laukkua) here?

Finnish distinguishes total vs partial / ongoing objects:

Genitive object (like laukun) → total action, complete event, whole thing affected.
Partitive object (like laukkua) → incomplete, ongoing, repeated, or partial action, or indefinite quantity.

With ottaa:

Otan laukun. – I take the (whole) bag.
Otan laukkua. – would sound strange with bag; grammatically it suggests an ongoing/incomplete action, or some unspecified amount of “bag”, which doesn’t fit well.

But with something like food:

Otan leivän. – I take the (whole) loaf / piece of bread.
Otan leipää. – I take some bread (an unspecified amount).

So in Minä otan laukun sohvan vierestä, using laukun (genitive) fits a complete, one-time action on the whole bag.

How do I know that sohvan vierestä is “from next to the sofa” and not “from the sofa’s side” in a more literal English sense?

In Finnish, combinations like [genitive noun] + vieressä / vierestä / viereen are fixed postpositional phrases meaning positional relations:

sohvan vieressä – next to the sofa
sohvan vierestä – from next to the sofa
sohvan viereen – to next to the sofa

Even though literally you might think "from the sofa’s side", idiomatically it just means from beside / from next to the sofa. That’s how native speakers understand it automatically.

What’s the difference between otan here and something like otan mukaan or otan pois?

All use the verb ottaa, but the added words change the nuance:

otan laukun sohvan vierestä – I take the bag from next to the sofa (neutral take; context decides if you keep it, move it, etc.)
otan laukun mukaan – I take the bag with me.
otan laukun pois sohvan vierestä – I take the bag away from next to the sofa (emphasises removing it from there).

You could combine them:

Otan laukun pois sohvan vierestä. – I take the bag away from next to the sofa.
Otan laukun sohvan vierestä mukaan. – I take the bag from next to the sofa with me.

In your original sentence, otan by itself is enough to express that you pick the bag up from that place.

Is the Finnish present tense otan used only for “I take”, or can it also mean “I will take”?

Finnish present tense often covers both present and future meanings. Context decides which is intended.

Nyt otan laukun sohvan vierestä. – Now I’m taking the bag from next to the sofa.
Huomenna otan laukun sohvan vierestä. – Tomorrow I will take the bag from next to the sofa.

There’s no separate “will” form; otan can mean I take / I am taking / I will take depending on the time expression and context.

Are there any sound or spelling changes in laukku → laukun and sohva → sohvan I should notice?

Yes, they show regular patterns:

laukku → laukun
- Just add -n for the genitive: laukku + n = laukun
- No consonant gradation here; kk stays kk in the stem, but in writing it appears as k before -n because the stem is lauku-.
sohva → sohvan
- Also just add -n: sohva + n = sohvan
- No changes inside the word.

These are straightforward genitive singular forms, used here because laukun is a total object and sohvan stands before a postposition (vierestä).