Electronic – Headphone volume control works for one speaker only

The writeup you linked to doesn't say much useful, but it appears these are bare speaker-type headphones (guessing from the size and shape). That means they are probably small speakers with 4 or 8 Ohms impedance.

You don't want to put a pot in line with speakers. That wastes power, doesn't present the right load to the amplifier, and probably messes up the frequency response due to the impedance change. The best place to put a volume control is in the signal path, not the power path. This means put it at the input of the amplifier that drives the headphones.

Whatever is driving the amplifier input is probably a "line" output. These usually have a few 100 Ohms impedance with a nominal 1V signal. A 1 kΩ logarithmic taper pot would be about right. Nowadays logarithmic tapers are harder to find because old fashioned analog pot volume controls aren't used that much. Nowadays the signal is handled digitally somewhere anyway, so the volume control is done by a digital multiply. If you can't find a logarithmic taper pot, it's not that big a deal. A linear taper will have a lot of change at the low volume end and not much at the high volume end, but for just setting a comfortable headphone volume it's probably good enough.

You can make a linear pot non-linear by putting another resistor accross the output. This doesn't make it logarithmic, but should spread the volume range out a little. Personally I wouldn't bother with this unless you've tried it directly and really didn't like the result.

As for avoiding hum and noise in audio, make sure everything is shielded. If necessary, mount the pot in a small metal box with the box grounded to the bottom lead of the pot, which should also be the ground for the input and output cables.

What you are missing is that the pot is wired such that it produces a ratio of the input signal with the ratio varying from 0 to 1 accross the full sweep of the pot. This is why the 5 kΩ and 10 kΩ pots resulted in the same full volume.

The pot achieves this by being a resistor divider. It does not work by adding resistance in series with a signal. A resistor divider looks like this:

The output will be R2/(R1+R2) of the output. In the case of a pot, R1 and R2 are one continuous resistor with a mechanical wiper picking off OUT at some point along this resistor. The three pins of the pot are the two ends of this resistor and the wiper tap. Therefore, R2 will vary from 0 at no volume to (R1+R2) at maximum volume. Also, R1+R2 is always fixed, and is the resistance value specified for the pot. In your "5 kΩ" pot, for example, R1+R2 is 5 kΩ, which is the value of the physical resistor that the wiper slides over.

At half volume, for example with the 5 kΩ pot, R1 and R2 are each 2.5 kΩ. OUT is half of whatever signal is applied at IN. Note that since everything is ratiometric, you get the same answer whether the total pot resistance is 5 kΩ or 10 kΩ. This is why the volume levels didn't change.

The total pot resistance does matter in other ways to the driving circuit and whatever is using the signal at OUT. The 5 kΩ pot will require whatever is driving IN to provide twice the current than is necessary with the 10 kΩ pot. You don't know what exactly is driving IN and what its design constraints might have been, so it is best to replace the pot with one of the same value. It seems you got lucky in that whatever is driving IN can cope with the 5 kΩ load, but it could just as well have started clipping, otherwise distorting, or have the frequency balance different.

The crackling and the fact that you got sudden jumps in volume were due to the old pot being worn out. As pots age, dirt and oxidation accumulates on the surface of the resistor where the wiper slides over it. The resistor itself can also get worn down due to mechanical abrasion by the wiper. The wiper sometimes making good contact and sometimes not can sound like crackling, especially when the pot is being turned. Dead and worn out spots on the resistor can cause sudden jumps. These are all common failure modes of pots.

This is one area where construction quality makes a big difference. El-cheapo pots wear out a lot faster and may not be as well sealed against dirt or the materials are more prone to oxidation. If you want long-lived mechanical volume controls, you have to spend the money on good quality pots.

This is also one reason these things are done digitally nowadays. You can get a microcontroller to handle the audio stream digitally for less than the price of a top quality volume control. The digital multiplies inside the micro don't wear out, crackle, or drift over time.