Technically, movement happens square-by-square. If something happens when you reach one square, that can change how you decide to spend the rest of your movement. So if you used Sidestep to avoid your attacker, but they still have sufficient movement to reach you, then they just have to keep moving towards you to make their attack. Even with Combat Reflexes, you cannot take more than one attack of opportunity per “provocation,” so the rest of their movement won’t provoke from you again and you won’t be able to use Sidestep again.
Unfortunately, the rules don’t come out and say this. However, the rules also don’t specify anything about actions “ending” per se. Nothing formally ends your move action aside from performing a standard action, or otherwise engaging in an action that cannot occur in the middle of a move. When someone moves from a square 10 feet from you to a square adjacent to you—when you take your attack of opportunity—they’re still in the middle of their move action. As they are still “moving,” they can just keep moving. The only limitation is their movement speed—which is defined by “you can move up to your movement speed.” No rule in the game says or suggests that you move by choosing a location within your speed and then just move their without any opportunity to change anything about what you’re doing.
Still, if they’re out of movement, you can avoid their attack.
This probably also applies to charging: they can (assuming they have movement available) decide to abort their charge, and step towards you, but their attack no longer counts as part of a charge. If they have already moved their movement speed or more (since charges allow moving double your speed), then obviously they cannot—though they can continue running in the direction they were, or charge into someone behind where you were, if someone is available.
Spring Attack doesn’t really come into play—you still only get one standard attack in the middle of your movement with Spring Attack, so if you haven’t done so yet, you still can (but you could even without Spring Attack; the feat only affects whether you can move after the attack). If you have already attacked, then of course you cannot attack again, though with Spring Attack you can continue to move.
Note that Sidestep gets much better with Karmic Strike or (better) Robilar’s Gambit, because these allow attacks to provoke from you—allowing you to Sidestep and potentially avoid further attacks (though they can still take a 5-foot step mid-full-attack if they haven’t moved that round). There, because they have committed to an attack, they aren’t able to regain that (attacks into squares where an opponent isn’t always miss). Note also that these pair well with Stormguard Warrior and Evasive Reflexes, though those don’t pair as well with Sidestep (since they hinge on attacks of opportunity you don’t take).
