I was researching about the SharePoint Client Object Model and REST but I am confused which one is strongly typed.
ASP.Net web services isn't strongly typed.
Most other objects in the other methods of interacting with SharePoint are strongly typed, however there are functions that can return objects that aren't strongly typed, but these link back to web services.
Here is a table that lists the differences for you: Data Access for Client Applications
Depends on what you mean by strongly typed.
The Client Side Object Model contains a lot of classes for working with the SharePoint objects, and these are strongly types. But the moment you start working with the content of lists, then you have to know or investigate the type of columns at runtime.
The REST interface is all XML/JSON are therefore only strings. But the proxy generated by visual studio creates wrappers around your list/content types which are strongly typed.
So in general I'd recommend using REST for accessing/modifying the content of lists/libraries and CSOM for the rest.