How to audit users connections via ODBC to all dbs in SQL Server 2008 R2
Now I would like to audit those connections - when they are happening and to which database.


If you want to audit on an ongoing basis then a server side trace will do the job.

Below is how you will script out from Profiler 





Entire SCRIPT :

/****************************************************/
/* Created by: SQL Server 2014 Profiler          */
/* Date: 06/18/2014  04:52:30 PM         */
/****************************************************/


-- Create a Queue
declare @rc int
declare @TraceID int
declare @maxfilesize bigint
set @maxfilesize = 5 

-- Please replace the text InsertFileNameHere, with an appropriate
-- filename prefixed by a path, e.g., c:\MyFolder\MyTrace. The .trc extension
-- will be appended to the filename automatically. If you are writing from
-- remote server to local drive, please use UNC path and make sure server has
-- write access to your network share

exec @rc = sp_trace_create @TraceID output, 0, N'InsertFileNameHere', @maxfilesize, NULL 
if (@rc != 0) goto error

-- Client side File and Table cannot be scripted

-- Set the events
declare @on bit
set @on = 1
exec sp_trace_setevent @TraceID, 14, 1, @on
exec sp_trace_setevent @TraceID, 14, 9, @on
exec sp_trace_setevent @TraceID, 14, 10, @on
exec sp_trace_setevent @TraceID, 14, 3, @on
exec sp_trace_setevent @TraceID, 14, 11, @on
exec sp_trace_setevent @TraceID, 14, 6, @on
exec sp_trace_setevent @TraceID, 14, 7, @on
exec sp_trace_setevent @TraceID, 14, 8, @on
exec sp_trace_setevent @TraceID, 14, 12, @on
exec sp_trace_setevent @TraceID, 14, 14, @on
exec sp_trace_setevent @TraceID, 14, 26, @on
exec sp_trace_setevent @TraceID, 14, 35, @on
exec sp_trace_setevent @TraceID, 14, 64, @on
exec sp_trace_setevent @TraceID, 15, 3, @on
exec sp_trace_setevent @TraceID, 15, 11, @on
exec sp_trace_setevent @TraceID, 15, 6, @on
exec sp_trace_setevent @TraceID, 15, 7, @on
exec sp_trace_setevent @TraceID, 15, 8, @on
exec sp_trace_setevent @TraceID, 15, 9, @on
exec sp_trace_setevent @TraceID, 15, 10, @on
exec sp_trace_setevent @TraceID, 15, 12, @on
exec sp_trace_setevent @TraceID, 15, 13, @on
exec sp_trace_setevent @TraceID, 15, 14, @on
exec sp_trace_setevent @TraceID, 15, 15, @on
exec sp_trace_setevent @TraceID, 15, 16, @on
exec sp_trace_setevent @TraceID, 15, 17, @on
exec sp_trace_setevent @TraceID, 15, 18, @on
exec sp_trace_setevent @TraceID, 15, 26, @on
exec sp_trace_setevent @TraceID, 15, 35, @on
exec sp_trace_setevent @TraceID, 15, 64, @on
exec sp_trace_setevent @TraceID, 17, 1, @on
exec sp_trace_setevent @TraceID, 17, 9, @on
exec sp_trace_setevent @TraceID, 17, 10, @on
exec sp_trace_setevent @TraceID, 17, 3, @on
exec sp_trace_setevent @TraceID, 17, 11, @on
exec sp_trace_setevent @TraceID, 17, 6, @on
exec sp_trace_setevent @TraceID, 17, 7, @on
exec sp_trace_setevent @TraceID, 17, 8, @on
exec sp_trace_setevent @TraceID, 17, 12, @on
exec sp_trace_setevent @TraceID, 17, 14, @on
exec sp_trace_setevent @TraceID, 17, 26, @on
exec sp_trace_setevent @TraceID, 17, 35, @on
exec sp_trace_setevent @TraceID, 17, 64, @on
exec sp_trace_setevent @TraceID, 10, 9, @on
exec sp_trace_setevent @TraceID, 10, 2, @on
exec sp_trace_setevent @TraceID, 10, 10, @on
exec sp_trace_setevent @TraceID, 10, 3, @on
exec sp_trace_setevent @TraceID, 10, 6, @on
exec sp_trace_setevent @TraceID, 10, 7, @on
exec sp_trace_setevent @TraceID, 10, 8, @on
exec sp_trace_setevent @TraceID, 10, 11, @on
exec sp_trace_setevent @TraceID, 10, 12, @on
exec sp_trace_setevent @TraceID, 10, 13, @on
exec sp_trace_setevent @TraceID, 10, 14, @on
exec sp_trace_setevent @TraceID, 10, 15, @on
exec sp_trace_setevent @TraceID, 10, 16, @on
exec sp_trace_setevent @TraceID, 10, 17, @on
exec sp_trace_setevent @TraceID, 10, 18, @on
exec sp_trace_setevent @TraceID, 10, 26, @on
exec sp_trace_setevent @TraceID, 10, 34, @on
exec sp_trace_setevent @TraceID, 10, 35, @on
exec sp_trace_setevent @TraceID, 10, 64, @on
exec sp_trace_setevent @TraceID, 12, 1, @on
exec sp_trace_setevent @TraceID, 12, 9, @on
exec sp_trace_setevent @TraceID, 12, 3, @on
exec sp_trace_setevent @TraceID, 12, 11, @on
exec sp_trace_setevent @TraceID, 12, 6, @on
exec sp_trace_setevent @TraceID, 12, 7, @on
exec sp_trace_setevent @TraceID, 12, 8, @on
exec sp_trace_setevent @TraceID, 12, 10, @on
exec sp_trace_setevent @TraceID, 12, 12, @on
exec sp_trace_setevent @TraceID, 12, 13, @on
exec sp_trace_setevent @TraceID, 12, 14, @on
exec sp_trace_setevent @TraceID, 12, 15, @on
exec sp_trace_setevent @TraceID, 12, 16, @on
exec sp_trace_setevent @TraceID, 12, 17, @on
exec sp_trace_setevent @TraceID, 12, 18, @on
exec sp_trace_setevent @TraceID, 12, 26, @on
exec sp_trace_setevent @TraceID, 12, 35, @on
exec sp_trace_setevent @TraceID, 12, 64, @on
exec sp_trace_setevent @TraceID, 13, 1, @on
exec sp_trace_setevent @TraceID, 13, 9, @on
exec sp_trace_setevent @TraceID, 13, 3, @on
exec sp_trace_setevent @TraceID, 13, 11, @on
exec sp_trace_setevent @TraceID, 13, 6, @on
exec sp_trace_setevent @TraceID, 13, 7, @on
exec sp_trace_setevent @TraceID, 13, 8, @on
exec sp_trace_setevent @TraceID, 13, 10, @on
exec sp_trace_setevent @TraceID, 13, 12, @on
exec sp_trace_setevent @TraceID, 13, 14, @on
exec sp_trace_setevent @TraceID, 13, 26, @on
exec sp_trace_setevent @TraceID, 13, 35, @on
exec sp_trace_setevent @TraceID, 13, 64, @on


-- Set the Filters
declare @intfilter int
declare @bigintfilter bigint

exec sp_trace_setfilter @TraceID, 10, 0, 7, N'SQL Server Profiler - 7fd54d82-f62b-4c99-8e02-ff0aa8d1d418'
-- Set the trace status to start
exec sp_trace_setstatus @TraceID, 1

-- display trace id for future references
select TraceID=@TraceID
goto finish

error: 
select ErrorCode=@rc

finish: 
go


If you want to just see who is connected now then you can use DMVs to look into 

The NULL in dbid (below query) indicates that those queries are Ad Hoc queries.

SELECT cr.DatabaseName
    ,s.session_id
    ,s.host_name
    ,s.program_name
    ,s.client_interface_name
    ,s.login_name
    ,s.login_time
    ,s.nt_domain
    ,s.nt_user_name
    ,c.client_net_address
    ,c.local_net_address
    ,cr.ObjName
    ,cr.Query
FROM sys.dm_exec_sessions AS s
INNER JOIN sys.dm_exec_connections AS c ON c.session_id = s.session_id
CROSS APPLY (
    SELECT db_name(dbid) AS DatabaseName
        ,object_id(objectid) AS ObjName
        ,ISNULL((
                SELECT TEXT AS [processing-instruction(definition)]
                FROM sys.dm_exec_sql_text(c.most_recent_sql_handle)
                FOR XML PATH('')
                    ,TYPE
                ), '') AS Query

    FROM sys.dm_exec_sql_text(c.most_recent_sql_handle)
    ) cr
--where s.nt_user_name = '' -- filter here your user name 
where s.session_id &lt;&gt; @@SPID
ORDER BY c.session_id