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In my world there are androids.

These robots look just like humans; you cannot tell them apart from a real person by looking at them, inspecting their bodies etc.

To attain this they need some mimicry of human physiology. Making a skeleton is easy but what about muscles? Muscles are probably the most evident feature other than the skin. Are there artificial muscles that can mimic humans' in terms of appearance?

They must feel like muscles: squishy, no clanking sounds, at least strong enough to move the body of the robot. I do not care what they look like, as they are covered by the skin.

How might they have these muscles?

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Yes, there are(in theory, and at some scale in lab)

This video Giant Stroke Artifical Muscles exactly about that stuff you are looking for, for same purposes you looking for, some very early early stage demos included.

Possible theory how some stuff might work: Carbon Nanotube Torsional Actuator Mechanism

This one if done on finer scale or covered with decorative layer also might be used:
Hydraulic McKibben Muscles

This interesting PVC_Gel_Artificial_Muscle
although need some technical imagination and a bit of fantasy.

This can be used to at least to mimic under skin movements Elastomeric Escapisms - Electroactive Polymers

This theory Fishing Line Artificial Muscles simple, cheap.
This is how it works in lab Artificial Muscle Fibre

Overall this direction of researches is researched, exactly for things like you mention.

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The thing you wish for already exists, Nitinol wires, otherwise known as "muscle wire". From the following link:

"Muscle Wire" is the perfect name for this product because it can be described exactly as it sounds: It is a unique type of wire that acts like the muscles in our bodies. Muscle Wire is an extremely thin wire made from Nitinol (a nickel-titanium alloy) that is known for its ability to contract when an electric current is applied.

Although thin and lightweight, one of the most amazing things about Muscle Wire is that they can lift many times their weight and are able to do 100 times more work per cycle than the human muscle. This material is easy to use, small in size, operates silently, has a high strength-to-weight ratio, and is easily activated using AC or DC power. This technology is ideal where mechanics require minimization, such as electronic textiles projects, robotics or nano-applications.

Either run current through or place these wires in hot water, and they can contract by 5%, and then expand to its full length again once cooled down, or when disconnected from the power source.

https://www.jameco.com/Jameco/workshop/ProductNews/musclewire.html

You can use those as a core, then pad them out with a gel or some other material (perhaps even wrapping each wire in a tube) to make the muscles feel human to the touch through the android's skin.

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Nitinol muscle wire (also named as shape memory actuator wire) presents many intriguing possibilities for robotics. Nitinol actuator wires are able to contract with significant force, and can be useful in many applications where a servo motor or solenoid might be considered.

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Well, they exist already, apart from the 2 mentioned above this one, which acts like almost a human muscle. In fact they are being researched as artificial muscles

https://en.wikipedia.org/wiki/Electroactive_polymers

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Amazingly enough, if you wanted to, you could make a robot with real muscles by growing live muscle cell cultures over a metal skeleton. In fact, someone already did just that.

That's a robotic stingray powered by rat heart muscle cells. Bio-robotic engineering at its finest.

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