help someone [do]/[to do]/[in doing]/[on doing] something?

Given the following sentences:

• They helped us frame some experimental evaluations.
• They helped us to frame some experimental evaluations.
• They helped us in framing some experimental evaluations.
• They helped us on framing some experimental evaluations.

Are all them grammatically correct or not? Are there any semantical nuances introduced by each alternative (and why), or do they mean exactly the same? Are there any other alternatives besides these 4 to convey the same meaning? Finally, which alternative is the best one, or does it depend on the context or writing style?

Solution 1:

The first one is normal. The second one sounds a little more formal. I would avoid the last two as they sound a little awkward.