"I am eating soup."

Translation: Jem zupę.

[uq.]

it's not "zupa" because it's accusative case and the verb "jem" is doing something to the noun "zupa".

flies away

[mihxal]

yes

[RicardoPotozky]

Its so weird for me to say "eat soup" instead of "drink soup"

[kurtkadiora]

In Poland when You use cutlery - You eat.

[va-diim]

For me it's the opposite. It feels strange to say "I'm drinking soup."

[Yola448704]

There are some clear soups you can drink. They are served
in cups or mugs for that purpose: clear red borscht (barszcz
czerwony czysty), clear broth (rosół, bulion).

[va-diim]

We have those in Russian too! Rassol'nik, cholodnyj borś, zʲelionyj borś, buľjon! Interesting!

[DebbyTeresa]

Yum. Barszcz jest smaczne.
Smaczny. Dziękuje va-dim. :)

[va-diim]

smaczny*

[KingNodding]

How would I say "I am eating tomato soup?" Is it like italian where you say tomato after soup?

[alik1989]

Jem zupę pomidorową.

The noun precedes the adjective here, because pomidorowa is not a secondary or temporal property, but a classifier.

[Alex_DC]

Is "Ja jem zupę" correct? Is it redundant?

[va-diim]

Yes it's redundant, unless you're emphasizing ja.