It looks like EZConnect can't connect for whatever reason (3a works/3b doesn't). You can try adding "ezconnect" to NAMES.DIRECTORY_PATH in the sqlnet.ora file. Hopefully that will make 3b from @Albert Godfrind's answer work.
The LDAP connection may fail from QGIS because you have something like the Oracle Instant Client somewhere in the path before your C:\OraClient11g\ client. In that case, sqlplus and tnsping would get loaded from the C:\OraClient11g\ client, while QGIS would load the other client that is missing the sqlnet.ora file. You can set the the variables ORACLE_HOME and TNS_ADMIN to tell the Oracle client to load the admin directory that it specifies, rather than the default relative path. Try setting these variable to force Oracle to use the same admin dir that sqlplus is using. Start QGIS from the command line after setting:
SET ORACLE_HOME=C:\OraClient11g\product\11.2.0\client_1
SET TNS_ADMIN=C:\OraClient11g\product\11.2.0\client_1\NETWORK\ADMIN
NOTE: I'm not sure if TNS_ADMIN is going to be just for TNS Names looks up, or if the client will load the sqlnet.ora file and use LDAP. Technically, I think ORACLE_HOME will be enough, and you don't actually need the TNS_ADMIN variable or tns_names.ora file.
I got this to work with TNS_NAMES by setting the TNS_ADMIN variable, then starting QGIS 2.4.0. I created the connection by only setting the Database, Username and Password values in the "Create a New OGR Data connection" dialog.
The version of QGIS that I have does have the instant client included in the bin folder, so you wither need to set TNS_ADMIN to use tns name conenctions, or create the Network/admin/ folders in the QGIS bin folders and copy your tnsnames.ora and sqlnet.ora file into it.
It looks like if you set the Host values in the connection dialog, QGIS tries to use an ezconnect connection.
Best Answer
You can get
ogr_sde.dllfrom the MapServer download. If you grab the zip file, it will be ingdalplugins\ignored\directory.Instructions for connecting to SDE through GDAL/OGR can be found here.