To successfully run PL/SQL Developer on wine you need to follow this steps:
0. Review associated bugs and limitations of chosen version and vote for them;
1. Install the latest possible wine version. Please note, in versions 1.3.22 and 1.3.23 there is regression, so do not use them;
2. Download Oracle Instant Client 32bit windows, version 188.8.131.52.0. Higher versions currently hang on use.
3. Unzip it in your drive c oracle directory, presumably .wine/drive_c/oracle;
4. Copy there tnsnames.ora and sqlnet.ora , where your database connection strings are described;
5. Install PL/SQL Developer as usual;
6. When running PL/SQL Developer you need to pass some environment variables to show where Oracle client lives and some language variables: env LC_ALL=bg_BG.UTF-8 ORACLE_HOME="C:\ORACLE" NLS_LANG="BULGARIAN_BULGARIA.CL8MSWIN1251" TNS_ADMIN="C:\ORACLE" wine "C:\Program Files\PLSQL Developer\PLSQLDev.exe"
This is the commandline string I use for Bulgarian locale and you should change it for your case.