I want to use some glue to secure this circuit. Is there any types of glue that I can use to secure this circuit without pluging up the holes on this solderless breadboard rendering the nodes disfunctional?
Hot melt. Easily removable when you no longer want it. If "permanent" E6000/old Goop from Eclectic (http://eclecticproducts.com/products/e6000/ ). It needs to cure overnight, but after that, it sticks better than snot.
If you are referring to the solderable boards with the same layout as solderless boards, they are great, and there are other suppliers of similar boards with plated through holes.
That is all I use now, unless it is really very temporary.
You, do not want to make an audio amplifier circuit on a solderless breadboard because the rows of contacts are intermittent and their capacitance between them and the long wires all over the place cause oscillation. The rows of contacts and long wires all over the place are antennas that pickup hum and all kinds of interference.
The cheap little speaker will sound harsh and tinny.
The cardboard enclosure is not solid enough and will vibrate with sounds from the speaker which will cancel some audio frequencies.
I have made thousands of audio, video, radio and digital circuits compactly soldered together on stripboard and they all had no interference and worked perfectly. The strips were planned to be short and were cut to length at a hole with a drill bit. Only one wire or pin for each hole on a copper strip.
Here is an example of a circuit made on stripboard: