The best configuration is what 57Gregy said (it's now set as a MME, I'd like to know more about the WDM in comparison)...
although the Sonar's playback makes my signal uglier with these weird noises...
 
Thank again!

NO NO NO.. that's the worst thing you can do. MME mode is terrible. 
Tascam has good drivers you will be crippled if you do not use them.
 what you need to do to fix your issue which is make Sonar grab the Tascam ASIO driver. 
You need to follow above advice,, minus running the wave profiler which has nothing to do with ASIO mode. That is only used if you do not have ASIO drivers.  

Cactus Music- It really did sound terrible, and it doesn't work anyway...
I start conside not even trying this DAW... Luckily the TASCAM US-4X4 comes with an Abelton Live 9 Lite as well!