Backup, backup, backup if at all possible to protect your data.
If you can get EtreCheck downloaded and run, it would be useful to see the output
<https://discussions.apple.com/docs/DOC-6174>
Look at Applications -> Utilities -> Activity Monitor to see if there are any processes that are hogging the CPU.
Look in the Applications -> Utilities -> Console logs to see if there are frequently repeating log entries that may indicate a process starting, failing, starting, failing, starting, failing, wash, rinse, repeat. This kind of activity would not show up in Activity Monitor.
If your data is safely backed up, you can try a clean install. Or if you can partition your disk to give yourself a 20 to 50GB partition, install a clean OS X into that and see if it works OK there. Of you you have an external disk you can erase, install a clean OS X on that (it will by definition run slower because it is running over USB, but some behaviors are not going to be affected by the disk speed).