Hey Champ, I had a similar experience the first time I changed my oil to my 'new to me' RC51.
Get rid of that engine oil, try Mobil-1 4T 10w-40 @ about $12/qt. or my favorite, Honda HP4S 10w-30 @ about $15/qt.
Get a new filter too. Mobile1 offers 2 different filters for the rc51, I use the M1-110. It's a bit longer than the M1-108. Both are listed for our bike. Or I also use the Honda OEM filter. I mention the Mobil1 oil and filter because it's easily available in all the AutoZones around here. You don't have to go to a dealership.
Change out your clutch fluid too, make sure to only use brand new DOT4 brake fluid.
Unless you have other problems, this should make your shifts smooth again.