Suddenly, out of nowhere, it came and grabbed one of them. They tried to follow but whatever it was it was too fast to catch up to. All they could do was listen as their friends cries became weaker and eventually stop. And wait until it would catch them. 

There's many ways to do this but you would need at least rogue lvl 2 (for cunning action) and preferably barbarian at level 3 (totem warrior, Elk!) to get it started properly. 

Here's what we WANT though: 

Stats: We need Dexterity and Strength at minimum 13 for the multiclass, though I think you'd want at least 14 Strength (preferably a bit more since).
Race: There are some options, honestly I think anything works. Variant human for the extra feat would be nice, extra strength and such would be good and woodelf 35 base movement (or half elf taking that woodelf trait) would be nice. 
Classes: 
Barbarian: Path of the totem warrior (Elk).
Rage: This gives us advantage on Strength checks. 
Totem spirit, Elk: This gives us 15' extra base movement during rage. 
Extra attack, Fast movement (level 5): At level 5 barbarian we get an extra attack for an additional chance of a grab but more importantly we get 10' extra base movement.

Rogue: Scout
Expertise (Athletics): Double proficiency for athletics is worth more than a high strength. Dash as a bonus action! 
Cunning action: Dash as a bonus action!
Skirmish: This is the reason we want the Scout archetype; We can use our reaction to move half our movement when an enemy ends their turn within 5' of us. This doesn't provoke attacks of opportunity.
Superiour mobility (level 9 scout): Another 10' of movement, although it's a bit high leveled.

Disclaimer: Technically an Eagle totem barbarian also gets dash as a bonus action with the added bonus of giving disadvantage on attacks, but I think the extra 15' movement is more fun. I'm sure this could be built around though.

Feats: 
Mobility: Another 10' movement. Also when using Dash we ignore difficult terrain penalties to movement. 
Wood elf magic/magic initiate: For the Longstrider spell that gives us another 10' movement for an hour with no concentration (since we can't do that in rage). 

Optional feats;
Athlete: For full climbing speed.

What we have: 
While it probably works decent before this, I'll make an example of a level 9 character. Mainly because by then we can have all goodies (except the superior movement from rogue that would require around lvl 14). I also won't be doing the EXACT build because it's not necessary, but only go through the basic stuff. 

Elk totem barbarian (5), Scout (4).
Strength 14 (Can probably easily get more but just for the example).
Skills: Athletics (expertise). +10 Athletics (lvl 5-8 "only" +8). (advantage while raging). 
Feats: Mobility, wood elf magic.

Base movement: 55' (35' Wood elf or half elf with that trait, +10' mobility, +10' fast movement from barb). 
Base movement in rage: 70'
Base movement with Longstrider: 65' or 80' during rage. 
Dash (bonus action): x2 movement.
Skirmish (reaction, specific situations): Half base movement.
Moving grappled creature: Half base movement. 


What do we do with this? 
Ok, basically we have 160' movement raging and using our bonus action for dash (note that rage requires a bonus action as well so this takes a turn to setup if you want the hillarious movement. 
So, you run up to someone, grapple them, then run. We have +10 athletics and advantage on this. We have two attacks, so for the first one we just make a grapple. If you fail, you obviously try again with your second attack, otherwise you could push them down as well since it's also kinda funny. This has another advantage (namely that your friends get advantage if they are within 5').
Then you run. Yes, it's halved movement. No it doesn't matter really matter.
Let's say you start 60' away, this would leave you with 100' left. So you could drag the target 50' away. In addition if anyone ends their turn next to you, you get another 20' reaction movement because of skirmisher. 
In other words you could start 100' away and still drag your target out of melee range from it's friends. 
If you instead start next to someone, you can snatch them away for a total of 90'. This also means that each turn you drag them at least 30' away from friends DASHING after you. 60' if they don't dash. 
By RAW you can also get this extra 20' movement from your target ending their turn (since they end it within 5' of you). 

Why?
Cause it's dumb and funny. Also cause once you push them down you can either drag them to your friends, so they get advantage while you beat them up far away from friends, but even better, since they are prone you have advantage on attacks against them and until they manage to get out of your grip, you have 2 attacks with sneak attack each turn while you're running around dragging them. But mostly because it's funny.

What else?
Do it at night, anyone without darkvision will hardly even have time to see what happens before you and your target is gone. 

Barb/Rogue is actually one of my favorite combos. Be a Valenar Wood Elf and grab a Revenant Double Scimitar for the best finesse weapon in the game (you still use STR but it qualifies for Sneak Attack). Start Rogue, end RogueX/Barb 5.

• Advantage on demand with Reckless Attack so you can always Sneak Attack.
• Skill utility of a Rogue
• Huge Durability with Rage resistance and Uncanny Dodge, decent AC with medium armor
• Practically Fireball-proof with DEX save proficiency + Danger Sense + Evasion
• Stopping at Barb 5, your Extra Attack and Rage damage make up for the 3d6 Sneak Attack you lose from 5 levels of Rogue. Can attack a 3rd time with RDS or use Cunning Action
• Huge Movement as illustrated above
• All of this is independent of your subclass choices - mix and match for more goodies

The main weakness is your mental stats. You do get WIS save proficiency if you go all the way to Rogue15/Barb 5, but that's too late to really count IMO. Also although you can hit 17 AC easily with medium armor + RDS feat, it's pretty hard to push beyond that (aside from magical bonuses) without spending a lot of ASI's on DEX/CON for Unarmored Defense, and you will often be granting advantage to enemies. You can mitigate this a bit with your crazy mobility though. Overall just a really fun combination, and depending on your subclass choices you can create some really interesting character concepts.

Yeah, I mean I figured this one out while doing another build tbh. 

Next rogue barb im playing will probably go swashbuckler and not elk totem ;) but just thought it was a weirdly fun build so wanted to post it.

With advantage and expertise though, you get such high numbers you can basically have a decently low strength score and instead focus a bit more on mental stats if needed. I mean, I did the calculations up there with just 14 strength and +10 athletics with advantage is enough for most things tbh. Now unless you're doing point buy or arranged scores it might not matter as much though. 

But it's a really good combination to ensure you have sneak attack when you need it.