I am currently in the US with an I-20 that will be expiring on 20th April 2016. I'm planning on going to Toronto for a short trip on 5th April and is planning to also apply ESTA(my country is under the visa-waiver program) for my re-entry to US. Will there be any problems if there's an overlap in date for my ESTA and I-20?
There is no problem with having an ESTA and another type of non-immigrant status in parallel. This is because the ESTA is only an electronic pre-authorization for travel and as such is not a visa.
However, note that you cannot perform studies towards a degree without entering the US on a suitable visa type. So entering under the visa waiver program after having had an I-20 may look a bit suspicious to the immigration officer. Thus, it makes sense to bring documentation with you that shows that your purpose of entering the US is compatible with the visa waiver program.
Related questions (although only considering J-1 visas) are:
- Visa J-1 and Visa Waiver Program during grace period
- I had a J1 trainee visa, can I go to Canada and come back with an ESTA?
Also see this link to an official US embassy site, which mentions a case where having an ESTA and a visa in parallel is actually needed in the answer to question 14, so having them in parallel should be possible. I got the link from a comment for this question.