Potrzebuję więcej siły.

Because potrzebuję is the 1st person singular form of the verb potrzebować (to need).

• potrzebować = to need
• potrzebuję = I need
• the ending -ę shows I

So Polish does not need a separate word for I here, because the verb ending already tells you who is doing the action.

In Polish, subject pronouns are often omitted when they are obvious from the verb form.

So:

• Potrzebuję więcej siły. = I need more strength.
• Ja potrzebuję więcej siły. also works, but ja adds emphasis, like:
  • I need more strength.
  • As for me, I need more strength.

The version without ja is the most neutral and natural.

The dictionary form is potrzebować.

A few common forms are:

• potrzebuję = I need
• potrzebujesz = you need
• potrzebuje = he/she/it needs
• potrzebujemy = we need
• potrzebujecie = you all need
• potrzebują = they need

So the sentence is built from potrzebować in the present tense.

Because więcej is used for more in quantity or amount, while bardziej means more in the sense of more intensely / more to a greater degree.

Here you are talking about having a greater amount of strength, so:

• więcej siły = more strength

Compare:

• bardziej zmęczony = more tired
• bardziej interesujący = more interesting

So bardziej siły would be wrong here.

Because after więcej (more) the noun normally goes into the genitive case.

The basic form is:

• siła = strength

But after więcej it becomes:

• więcej siły = more strength

Also, the verb potrzebować often goes with a genitive object in standard Polish, so siły fits the grammar very naturally here.

Here siły is genitive singular.

From the noun:

• siła = nominative singular
• siły = genitive singular

So in this sentence:

• Potrzebuję więcej siły.
• siły = of strength / more strength

One small complication: siły can also be nominative plural in other contexts, but not here. In this sentence, it is understood as genitive singular.

Yes, you may hear that too.

There is a slight nuance:

• więcej siły = more strength, more power in a general/abstract sense
• więcej sił = more strength/energy reserves, often a bit more idiomatic in everyday speech

Both can sound natural depending on context. The sentence you were given, Potrzebuję więcej siły, is fully correct and clear.

No. Siła can be used in several ways.

It can mean:

• physical strength
• mental strength
• emotional strength
• inner strength
• even power in some contexts

So Potrzebuję więcej siły could mean:

• I need more physical strength.
• I need more inner strength.
• I need more energy to cope.

The exact meaning depends on context.

No, Polish word order is fairly flexible.

The most neutral order is:

• Potrzebuję więcej siły.

But you can move things around for emphasis, for example:

• Więcej siły potrzebuję. = It’s more strength that I need.
• Siły potrzebuję bardziej niż odpoczynku. = I need strength more than rest.

So the original sentence is the normal, neutral version.

A rough pronunciation guide for an English speaker is:

• Potrzebuję ≈ po-tsheh-BOO-yeh
• więcej ≈ VYEN-tsey
• siły ≈ SHEE-wih

A more accurate pronunciation is approximately:

• potrzebuję = poh-tsheh-BOO-yeh
• więcej = VYEN-tsehy
• siły = SHI-wih

A few useful sound notes:

• rz sounds like the s in measure
• ę at the end of potrzebuję is often pronounced more weakly in everyday speech
• si before a vowel-like sound is a soft sh-like sound
• Polish stress is usually on the second-to-last syllable:
  • potrzeBUję
  • WIĘcej
  • SIły

It is neutral.

That means it works well in:

• normal conversation
• writing
• personal situations
• serious or emotional contexts

It is not slang, and it is not especially formal either. It is just standard, natural Polish.

Sometimes, yes, but strength is usually the best default translation.

The noun siła can mean:

• strength
• force
• power

In this sentence, strength sounds most natural in English unless the context is specifically about electricity, politics, physical force, or some other special kind of power.