There's a lot to consider here but overall I would consider this feat to be OP compared to similar options in published material. Weapon design in 5th edition is nearly completely damage type agnostic, so the "slashing weapons only" stipulation provides little to no balance. The language surrounding shields is unclear but seems to be safely ignored.
With those points taken, we now have something that is built on the chassis of Sentinel, which is already a strong feat. On top of this, we're stacking a +1 to an ability score. In exchange for this +1, we're cutting the likelihood of the speed reduction, and limiting the targets of the Reaction attack triggered by a creature attacking an ally near you. It's also worth noting that you didn't specify this attack had to be a melee attack, opening up weird situational cases involving stuff like throwing handaxes at a target who has teleported to safety. For the purposes of this balance rundown I'm going to assume that was an oversight. I'll also assume the lack of a clause against recursion (like Sentinel now has) was an oversight as well.
Following the AC vs to-hit bonus progression, we can expect the speed reduction to trigger roughly 65-70% of the time the attack hits (this increases with magic items). Comparing this to Sentinel, where it occurs on every hit, we see that now roughly 42-49% of opportunity attacks will reduce speed to 0. Sentinel's likelihood is 65-70%, since its attack needs to hit to reduce speed as well. If the attack has disadvantage, the speed reduction for this falls to 0%, and for Sentinel it falls to 42-49%.
Now we have to weigh the relative value differences. There's the benefit of +1 Strength. This is massive, providing a possibility of +1 to every single to-hit and damage roll for the rest of the character's life, as well as Athletics checks and Strength saves. It also synergizes with this feat's other half, making the attack hit and speed reduction more likely. (In a more abstract fashion, we could treat it as a +0.5 to STR based rolls, and apply some sort of opportunity cost accounting for the period that the odd STR score could've been something else generating more value. But that seems excessive.)
We assess this sizable benefit against the detriment of a 15-20% decrease in likelihood of stopping a creature, a susceptibility to disadvantage, more specific targeting criteria on the bonus action attack, and not bypassing the Disengage action. I feel that the +1 heavily outweighs these relatively minor nerfs.
In comparison to other "half-feats", or feats that offer a +1 in an ability, this is also clearly extremely strong. Comparing it to Slasher, for example, shows that this is comprehensively better. Slasher's 10-foot speed reduction once per round is on par with a cantrip rider (it literally is one, see Ray of Frost). The critical feature is nice but triggers infrequently enough at most levels as to only slightly contribute to balance. This feat's good chance to stop an enemy in their tracks is a bit better than that on its own (the math on this is highly dependent on enemy movement and the Slasher's attacks per round, but leans towards Slasher being worse) and the Sentinel-style reaction attack on top pushes this into the "nearly always better than similar published material" range. An extra attack whenever an enemy isn't targeting you is just extremely strong, especially in the limited action economy of low level play.
D&D isn't really about some guy online explaining the math and comparing your stuff to published material in a vacuum though. This feat doesn't look to be game-breakingly OP, it's just imbalanced in comparison to what's already out there. If I was your DM and read this, I'd probably nerf some component of it (maybe remove the reaction attack) and let the rest fly, maybe providing a chance for your character to train and develop the part that I'd removed later in the campaign. Honestly I'd probably be more likely to allow this as-written than Lucky (PHB 167) at my table, and Lucky is in the book, so there's certainly precedent for OP stuff in published material as well.