Hello there,
Litz wire does not reduce skin effect. Skin effect is a consequence of nature and we cant easily change that. What Litz wire does reduce is the copper lost because of the skin effect. We could in fact find a large diameter wire that conducts the same as several smaller diameter wires, but the difference would be almost all the smaller diameter wires copper would be actually still conducting while most of the larger diameter wire copper would not be.
With one large diameter wire the skin effect might cause very little current flow in 90 percent of the inner cross section, meaning we just lost a wire of equal length but of smaller gauge (the inside non conductor part). That's a whole equivalent wire lost. But break that up into two smaller gauge wires and we see more of the copper in those two wires actually being used. So we end up with a smaller copper loss. If we break it up into even smaller pieces, we may see only 10 percent lost which is a much better figure. This kind of quality measurement would be known as the DC to AC resistance ratio.
Another way to think of it is if we had a large diameter copper wire and much of the inside part of the cross section was not conducting much, if we separated the inside part from the outside layer with an insulation layer, the inside wire would conduct more too and we'd still be using the same amount of copper. So Litz wire improves the AC current to copper ratio, which improves the AC conduction with no additional copper. Of course there is the complexity of producing the wire which would make it more expensive.
If you needed to wind a multiple turn inductor and you used Litz wire to avoid having to wire every single turn, you may find that the inductance isnt quite what you expect. That might be because Litz wire is wound in a very particular manner where the wires are twisted or arranged to equalize certain characteristics of the wire and that may cause less inductive interaction between turns. Normally an inductor is wound one turn after the other where each turn is next to the one right after it, the turns are not arranged in groups of several wound turns which lowers inductance, and the idea of an inductor is to get as much inductance in as small a space as possible. It might work, but not as good as a single turn coil, however it may reduce the side effect of capacitance which affects self resonance.