Saya tidak suka makanan yang terlalu berminyak.

A word-by-word breakdown is:

• Saya = I
• tidak = not
• suka = like
• makanan = food
• yang = that / which
• terlalu = too / overly
• berminyak = oily / greasy

So the structure is basically:

Saya + tidak suka + makanan yang terlalu berminyak
= I do not like food that is too oily

Because tidak is used to negate verbs and adjectives, while bukan is mainly used to negate nouns or noun phrases.

Here, suka means to like, so it is negated with tidak:

• Saya tidak suka = I do not like

Compare:

• Ini tidak enak = This is not tasty
• Ini bukan makanan saya = This is not my food

So bukan suka would be incorrect here.

Yang introduces a clause that describes a noun, similar to that, which, or that is in English.

In this sentence:

• makanan yang terlalu berminyak

literally means:

• food that is too oily

So yang terlalu berminyak describes makanan.

This is a very common Indonesian pattern:

• orang yang baik = a person who is kind
• buku yang mahal = a book that is expensive
• makanan yang terlalu berminyak = food that is too oily

This is an important difference.

• terlalu berminyak = too oily, with a negative sense
• sangat berminyak = very oily, more neutral as a description

So:

• terlalu suggests more than is good, wanted, or acceptable
• sangat just means very

Examples:

• Kopi ini terlalu manis. = This coffee is too sweet.
• Kopi ini sangat manis. = This coffee is very sweet.

In your sentence, terlalu makes it clear that the oiliness is a problem.

Berminyak means oily or greasy.

It comes from:

• minyak = oil
• berminyak = having oil / oily

The prefix ber- often gives the sense of having, wearing, or possessing something, depending on the word.

So:

• berminyak = having oil on it / oily
• berbulu = hairy / furry
• berdarah = bloody / bleeding

You do not need to translate ber- literally every time, but it is useful to recognize that it often helps form descriptive words like this.

Because makan is the verb to eat, while makanan is the noun food.

• makan = eat / to eat
• makanan = food

The suffix -an often helps form nouns.

Examples:

• makan = eat
• makanan = food

So in this sentence, you need the noun makanan, because you are talking about food, not the action to eat.

Yes. Aku is more informal, while saya is more neutral and polite.

• Saya tidak suka makanan yang terlalu berminyak.
  Neutral/polite, good in most situations

• Aku tidak suka makanan yang terlalu berminyak.
  Casual, natural with friends, family, or in informal conversation

A native speaker might choose either depending on the situation.

Indonesian often does not need a separate word for is / are in simple descriptions.

So:

• makanan yang terlalu berminyak

literally looks like:

• food that too oily

but naturally means:

• food that is too oily

This is normal in Indonesian. The linking verb to be is often omitted when describing something.

Compare:

• Dia cantik. = She is beautiful.
• Rumah itu besar. = That house is big.
• Makanan itu berminyak. = That food is oily.

It can be either, depending on context.

In Indonesian, nouns often do not have to show singular or plural explicitly. So makanan can mean:

• food in a general sense
• a food
• foods, depending on context

In this sentence, it most naturally means food in general:

• I don’t like food that is too oily

If you really wanted to emphasize plural, you could say makanan-makanan, but that is usually unnecessary here.

Usually, yang is the most natural choice here.

• Saya tidak suka makanan yang terlalu berminyak.
  = natural and standard

If you remove yang:

• Saya tidak suka makanan terlalu berminyak.

this may sound less clear or less natural, because yang neatly connects makanan with the description terlalu berminyak.

So for learners, it is best to keep yang in this kind of sentence.

Yes, a few alternatives are possible, depending on nuance.

Some examples:

• Saya tidak suka makanan berminyak.
  = I don’t like oily food.
  Slightly more general; it does not specifically say too oily.

• Saya kurang suka makanan yang terlalu berminyak.
  = I’m not very fond of food that is too oily.
  Softer and less direct than tidak suka.

• Aku nggak suka makanan yang terlalu berminyak.
  = casual spoken Indonesian
  nggak is an informal form of tidak

Your original sentence is a very natural standard Indonesian way to say it.