EF v1 has no direct support for OdbcConnection (in current release Microsoft ships EF-compatible providers for SQL Server and SQL Compact).
The reason for that is that EF requires the provider to supply metadata describing store types, built-in functions and primitive type mapping information - something that's not available through ODBC layer. There are also differences in SQL syntax supported by databases and the provider would have to compensate for those differences - again ODBC doesn't have enough information to do this in a general way.
If you want to target a specific database which has ODBC driver available, you can create EF-compatible provider by using the wrapping technique demonstrated in EF Sample Provider and EF Oracle Provider samples on MSDN Code Gallery.