Unable to connect Access to SQLlite via ODBC
Whats with all that copying dlls around - you don't need to do any of that. Just download the 32 bit version and double click on it - the driver will be installed. Then find the 32 bit ODBC Administrator (note there are 2 on 64 bit windows and only one is 32 bit), fire it up and create a DSN. You should see sqlite3 in the drivers tab.
DSNs are not there automatically, you have to create them yourself. There should be an "Add" button in the ODBC administrator. Then you select the type of driver "SQLite", and then configure the details in the next dialog.
A DSN normally contains all the configuration information needed to connect to a specific database instance so that all this - which may be different from one database system to the other - can be referenced by one name. That is where the name "Data Source Name" comes from.