Room treatment ideas for annoying external noises

disconnect refrigerator temporarily

Noise is out of control. Beg neighbors to stop hiring lazy landscapers who use leafblowers. 

Support any local attempts to ban leafblowers and enforce noise regulations.

Record dogs and play back barking when neighbors think they are going to have peace and quiet. Use supertweeter arrays to blast dogs with ultrasonics.

Another option -- just turn up the volume!

Improve the sound of your audio system.

When the audio sound is unnatural, human ears must adjust to that unnatural sound to hear clearly. Dog barking and construction sound are natural sound and they disrupt listener's concentration to unnatural sounds (audio sound) because human ears react to natural sound much easier.

If audio sound is truly natural, human ears don't need to do (adjust) anything for the audio sound. And there will be no listener's fatigue.

Alex/Wavetouch

What you are looking for is how to soundproof a room, not treat it. There is tons of information on Google and YouTube for you to see what is in your budget.