How to clean/remove distortion/noise in my LM1458 Op-Amp?
I'm not going to watch a video of some wiener building a circuit then try to extract the schematic from a blurry screen shot of a video, and you shouldn't either.  You need cleanly drawn schematics to work from, and a written explanation of the circuit function would be good, too.
The 1458 is a dual version of the 741, commonly known as "that piece of crap that people should stop using because there are so many much better alternatives."
The 741 cannot drive a 4 ohm speaker with any kind of power.  The datasheet for the ua741 gives the output resisitance as 75 Ohms.  This cannot really deliver any useful power to the speaker.
Regardless of how much power the 1458 could put out, that jiggery pokery with R1,R2, and C1, C2 that you've connected the speaker to would make it impossible to get any real amount of power through the speaker.
Your circuit diagram is hard to read.  You generally start on the left with the input and work your way to the right for the output.
Your circuit diagram makes no sense.  There are so many non-sensical parts that I can only assume you've copied the circuit incorrectly from a fuzzy video.


In short:

If you built the circuit as you've drawn it, then it is a wonder that your circuit does anything at all.  Expecting it to work correctly is just too much.



I would suggest you start with clear and correct circuits.
Here are two simple circuits that will be much easier to build:


Suggested circuit from the datasheet of the LM386  This is a simple IC that can directly drive a speaker.  Use the first circuit from page 5 of the linked document:

This is a stereo amplifier that can drive two speakers and still has fewer parts than that mess built out the 1458.  This amplifier can output 2.5Watts per channel, and can be built to provide 5Watts to one speaker.  See the circuits given in the Tea2025 Datasheet for more information.