Help + Noun + Ing-form or Infinitive
- Help my sister peel oranges.
- Help my sister to peel oranges.
- Help my sister peeling oranges.
- Help my sister with peeling oranges.
Which of the above is/are correct, and why are the others incorrect?
Grammatically, all the sentences are correct.
There are usually differences in implication depending on context. Subtle changes in meaning can be imparted by what is called semantics.
Note also that some forms/ constructs may be idiomatic in some places but not in others. So what sounds natural to some people may be odd to others. It is important to know the target audience in selecting the form of the sentence that suits best.
In many languages, grammatically similar sentences with different word order/ construct can also have different meanings, defined by usage and custom rather than language per se.
Say, for instance:
"Help my sister peel oranges." could suggest "show her how to do it"
"Help my sister to peel oranges." might imply "prepare the oranges so she can peel them"
"Help my sister peeling oranges." can indicate "I mean the one who is peeling oranges, not the other"
"Help my sister with peeling oranges." maybe seen as "do half the work"
None of these interpretations can be drawn, though, without knowing the cultural and pragmatic context.
Other prepositions …
Help my sister by peeling the oranges.
Help my sister in peeling the oranges.