As far I saw, if the phone already locked.. It does show on the lock screen by which finance service it has been locked with and phone is not usable..
If the emis are paid till the date before it was sold and there are emis remaining.. For samsung finance, there will be an app installed called samsung finance with administrative privilege which cant be uninstalled till the emis are cleared.. For tvs credit service you can check the tvs credit app in the device admin app ( attached image) .. For hdfc and hdb finance its mentioned in the original bill of the phone by which finance service it was financed with..
So key points to check before you buy from Olx is
1. If There are Any app installed with administrative privilege in Device admin app list (For Samsung Finance & TVS Credit Service - These 2 are Nasty..Cant unlock the phone in any way since the app doesn't let you Turn on USB DEBUGGING- My personal Experience)
2. For HDB & HDFC finance you need to check the Bill.. (I think For HDFC & BAJAJ , the buyer don't get affected if the Original buyer doesn't pay emis since there is no app to remote lock the phone) The Main Buyer will be solely responsible not for paying EMI