Overchannel definitely maximizes the base damage, Sneak Attack definitely applies, but Overchannel does not maximize sneak attack damage
Overchannel can maximize the damage roll(s) of any spell you apply it to:
When you cast a wizard spell of 1st through 5th level that deals damage, you can deal maximum damage with that spell.
Not only does using our ability to read tell us that this applies to any spell, but we even have developer commentary assuring us that that is, in fact, the correct reading:
If I Overchannel Bigby's Hand, this spell inflicts maximum damage every time it deals damage (ie on subsequent rounds)?
Overchannel. By RAW, it works as long as the spell lasts. Not exactly the intent (works only on the first turn), but it's functional.
So Shadow Blade, like Bigby's Hand and any other spell that does damage over more than one turn, benefits fully from Overchannel. Spells that result in enemies taking damage but don't actually deal any damage don't benefit from Overchannel, but that's not the sort of spell Shadow Blade is; the shadow blade is a spell effect so when you hit someone with it the spell is dealing damage as specified in its description. If you want to rule that the sword is a created object rather than a spell effect you can do that without violating the RAW, but that extension has counter-intuitive consequences like the sword being usable within an antimagic field for example.
Since this spell effect is also a weapon with the finesse property, you can sneak attack with it, assuming you meet the other requirements (e.g. having advantage on the attack roll or another qualifying situation).
The Sneak Attack feature says:
Once per turn, you can deal an extra 1d6 damage to one creature you hit with an attack if you have advantage on the attack roll.
You make this choice when you hit a creature with your attack. That's after you already used Overchannel and so the damage the spell deals is already maximized and this modification is done on top of that. Because Overchannel always happens first with Shadow Blade there's no way, even if you interpret Sneak Attack as modifying the base damage roll rather than adding an additional damage roll, for Sneak Attack to happen first and get maximized. This is the same logic as why, if you are affected by longstrider and then feign death your speed is 0 but if the spells affect you in the reverse order then your speed is 10'. Or, similarly, if you wear a belt that sets your STR to 19 and then get STR drained by a shadow your STR is now less than 19 but if you get STR drained to 1 STR and then finish attuning the belt your STR is 19. The order of operations with modifiers to rolls matters a lot. Maximizing the damage and then adding a variable amount can be very different than adding a variable amount and then maximizing the damage.
If you did use Sneak Attack first somehow, for the sake of argument, you still might not get the damage maximized because it is not clear whether the damage is part of the spell or not and your DM would have to pick. That is, your DM might say "Sneak Attack isn't from the spell, so it does not benefit from Overchannel" and they wouldn't be wrong, even though another DM might say "Sneak Attack damage is spell damage, so it does benefit from Overchannel". Both are interpretations compatible with the RAW.
Note that the typical 14th level Wizard/3rd level rogue making use of this trick is dealing 32+2d6 psychic damage each round with the blade from approximately 20 feet away until they drop the spell when they lose concentration while a typical 17th level wizard is dealing 2d6 less damage with bigby's hand from 120 feet away and a typical 17th level rogue has their capstone ability; game balance is not particularly upset by letting a rogue/wizard make use of the class features the rules grant them.
