I never really heard of the guy either so had no clue on his stances. Just looked some of them up (forgive me, it's long):
Economy:
•Converted Ohio's $8B deficit to $2B surplus. (Nov 2015)
•Balanced Budget Forever: promote constitutional amendment. (Feb 2015)
•Against ethanol subsidies, and all subsidies. (Apr 1999)
•No income taxes on small businesses up to $2M. (Feb 2015)
•Expand Medicaid; everybody has a right to God-given purpose. (Aug 2015)
•Opposes ObamaCare but not all public programs. (Aug 2015)
•Accepted ObamaCare's Medicaid expansion statewide. (Feb 2015)
•Limit collective-bargaining rights for public employees. (Mar 2015)
•Fix Social Security by lowering benefits. (Oct 2015)
•Voted YES on reducing tax payments on Social Security benefits. (Jul 2000)
Misc:
•Death penalty is consistent with justice & Christian values. (May 2015)
•Voted NO on funding for alternative sentencing instead of more prisons. (Jun 2000)
•Voted YES on more prosecution and sentencing for juvenile crime. (Jun 1999)
•More prisons, more enforcement, effective death penalty. (Sep 1994)
•Don't send mixed signals to kids by legalizing. (Oct 2015)
•Voted YES on prohibiting needle exchange & medical marijuana in DC. (Oct 1999)
•Voted YES on banning physician-assisted suicide. (Oct 1999)
•Member of the Tea Party movement. (Aug 2012)
•Defund Planned Parenthood, like we are trying in Ohio. (Sep 2015)
•Pro-life except rape & incest; supports litmus test. (Apr 1999)
Environment:
•Climate change is a real issue, but the extent is unproven. (Aug 2015)
•Voted NO on starting implementation of Kyoto Protocol. (Jun 2000)
•Strengthen Clean Water Act; increase federal grazing fees. (Nov 1996)
Education:
•I like the ideas in Common Core, but not the program. (Jul 2015)
•We need charter schools, with state oversight. (Jul 2015)
•$120 million student debt relief fund; plus online college. (Feb 2015)
•Voted YES on giving federal aid only to schools allowing voluntary prayer. (Mar 1994)
Religion:
•Bible stories are historical facts. (Jun 2010) (Believes Noah and the flood are factual historical events)
•Did earth come about on its own? Evidence says No. (Jun 2010)
•Separating church and state is goofy misinterpretation. (Jun 2010)
•Limited government supported by our Judeo-Christian ethics. (May 2006)
Foreign Policy / Trade:
•No more Syrian refugees in Ohio or anywhere in USA. (Nov 2015)
•Keep Iran accountable, WITHIN the existing Nuclear Deal. (Sep 2015)
•Fight ISIS with a coalition including US ground troops. (Jul 2015)
•No diplomatic relations with Cuba nor Vietnam. (Nov 1996)
•Supports NAFTA and GATT. (Nov 1996)
•It's a silly argument to ship 11M illegals back to Mexico. (Nov 2015)
•Seal the border with Mexico, support legal immigrants. (Jul 2015)
That is a small portion of his quotes and history from here:
http://www.ontheissues.org/John_Kasich.htm
According to PBS, here are some of his recent stances:
•Climate change is real. The EPA should not regulate emissions.
•Less prison time for nonviolent offenders. Focus on rehabilitation and treatment.
•Continue Common Core. Cut education spending.
•Allow undocumented immigrants to stay in the country legally. A path to citizenship is not preferable but may be part of compromise.
•Keep the federal Medicaid expansion. Repeal and replace the rest of the Affordable Healthcare Act.
•It’s time to move on from the same-sex marriage debate. Ban abortions after 20 weeks, with an exception if the life of the mother is in danger.
•Cut income and corporate taxes. Close some loopholes. Raise other taxes, including a state tax on fracking.
http://www.pbs.org/newshour/updates/john-kasich-believe-candidate-stands-10-issues/
He really is pretty moderate and has plenty of stances I could agree with (and plenty I don't). He can't keep his religion out of our government though so that sort of turns me off.