The deadline is Sept 21 for applying for the Undergraduate Research Scholarship (URS) and the International Research Grant for Undergraduates in the Arts and Sciences (for juniors in Honors): http://aschonors.osu.edu/opportunities/scholarships/undergrad
The deadline for applications and project advisor recommendations is Monday, September 21, and selections will be made by late November. The Honors Committee does not require that applicants be members of the Arts and Sciences Honors Program; however, the committee generally gives preference to students who are candidates for graduation with research distinction or with honors research distinction, because they have demonstrated the sort of academic ability and commitment which indicates the likelihood of success in completing a major research project. If you have questions, contact the Arts and Sciences Honors Office at 614 292-5104.
A list of Arts & Sciences majors is here: http://undergrad.osu.edu/academics/colleges-and-schools.html