Why is everyone saying this is an internet issue ._.
It's not. It's a basic tenet of Minecraft PvP, or at least MCSG's PvP. The natural reach in Minecraft is around 4-5 blocks, and MCSG has nerfed that reach to around 2-3 blocks. That explains why it happens more often on other PvP servers, and also shows that the range they are hitting you at is really not that extreme. It isn't lag that is allowing them to do this, it's skill and knowledge of the game mechanics, which the majority of the well known players in the community have a good grasp on.
Now, I think I know what your issue is when it comes to PvP. You know the general ideas behind some of the tactics that players employ, but not what actually makes them work. When you strafe, you can't simply run around to the side of them, they'll hit you while you're doing so, and, even if you succeed, they can simply turn and continue hitting you. Strafing is all about avoiding enemy attacks, but if you give your opponent room to think, then it won't work. You need to be constantly swinging while you strafe around them, constantly keeping them off balance and unable to hit you. If youdo successfully make it around to their side without being hit, then you can start jumping while hitting in order to get crits and thus deal more damage. However, this will increase the knockback of your blows, so you should try to hit them into a wall or something like that so that they'll be dazed and confused as opposed to being able to easily run away.
As to your second tactic: it doesn't work. If you stand still and wait for a person to come at you, you have no momentum, and can easily be steamrolled by a charging opponent. Jumping into combat has the effect of both increasing the knockback you deal, and also the amount you take. It also serves to increase your range slightly (compared to a still player at least), as your momentum is carrying you forwards faster than they can react. You also then have the opportunity to strafe around the still player and hit them to your heart's content. Standing still is never a good strategy.
Overall, I would just try to keep this in mind while you're trying to build up your PvP skill: Hit them a lot. Though Minecraft PvP has advanced considerably, that is still it's basic tenet. If you get more hits on your opponent than he does on you, you'll most likely be doing more damage, and end up winning a lot more fights. Practice just pure clicking speed. Make sure you can start a sprint quickly after hitting someone so you're able to quickly leap forwards and deal more damage after you knock someone back. Jump when you're in a safe position in order to get crits (this will make you more susceptible to knocback though, so be careful). And, however much you knock the alternate weapons, I would strongly advise learning to use them well. In the type of PvP environment we play in these days, those are absolutely essential to being a great player. Yes, I agree, you should not kill people with them and not show any skill, but if you use them SKILLFULLY, then they do nothing but improve your worth as a player (though people may rage at you and call you cheap for using it, any tactic that works is a good one).