1. We can make empty milk packs into new paper.

2. We can make empty milk cartons into new paper.

(Which expression is correct?)

3. We can make pieces of a soap bar into a big soap bar.

4. We can make pieces of bars of soap into big bars of soap.

(Which one is correct?)

5. Old plastic cups can be small flower vases.

6. Old plastic cups can be used as small flower vases.

7. Old plastic cups can be made into small flower vases.

8. Old plastic cups can be recycles to make small flower vases.

(Are the four expressions all grammatical?)

1 and 2 - cartons

3 and 4 - I'd rephrase a bit: We can make pieces of soap into a big bar of soap. [In fact, "of soap" at the end can probably be safely left out.]

5 - 8
All are grammatically correct. 6 is the most commonly used, I think. (8 needs a spelling correction - "recycled.")