Legacy SQL Activity and Contacts Dump Transfer
For contacts and activities you could use the built in import functions If you want to migrate/import entities for which there is usually no gui (such as events), you could try this extension: https://civicrm.org/extensions/api-csv-import-gui

I am not sure if it works for profiles though. You could of course use the Rest API as well and for example code a script to import everything but the first time this would probably take a while to get your head around.