What does it mean to say ( I’ll get right on it) if someone in a really terrible situation and being offered a help and he replied ( I ‘ll get right on it )
I'll get right on it is simply a way to say "I will do that as soon as possible." It just means that one will do a particular task promptly.
In your situation, if someone asked for help and someone said, "I'll get right on it." It means that they will try to get help as soon as possible for the person.
Also check https://idioms.thefreedictionary.com/ if you're confused on these idioms.