I'm sorry to say you just have to sit it out until the phases passes, and, yes, it is important to deal with it, but I'm afraid IME, toddlers, particularly when their speech is developing, it is an inevitable but unfortunate stage for some parents.
My ds1 is nearly 3 and is so much better but from about 20 to 23 months, he was horrendous - hitting, pushing and wailing if another child even so much looked at a toy he wanted (and he wanted EVERY toy). I remember with a shudder the time when I was heavily pregnant with dd and went to a soft play area - I spent the whole time removing him from each bit of the soft play as he hit and pushed his way through pretty much every child in the place until I broke down crying from all the horrid looks and occasional bitchy comments from the other mothers and took him home.
He abated briefly for a couple of months after that but has regressed on and off since then. His aggression is much more under control now as he understands the consequences much better, whereas before it was like trying to push jelly up hill with a fork. I know and understand his flash points, I've limited playdates to kids I know who don't wind him up and prefer to meet friends with kids in the park or somewhere a bit more neutral than a house. I avoid soft play if it is likely to be busy or he is tired. I actively seek out meeting up with people with older kids as he responds so much better to them and plays really nicely (eg. his two older cousins, 7 and 9).
ALthough I have no magic solution to stopping him hitting, some things have worked better than others - for example (and it may sound a bit cruel), I set up a couple of playgroup visits which I knew I could take him home from without leaving my friends disappointed if we left - if he went to hit another child I warned him that if he actually did it again we would go home. He did and we did. I did this on two separate occasions and it really seemed to make a bit of a difference. Now the threat of going home seems to work better than anything else. Whatever your style of dealing with it is, it's important for them to see you carry out whatever consequence you say.
It's was also helpful for me to read a bit about why toddlers respond like this - in a nutshell - when they are growing or reaching a new developmental milestone, this takes priority in the brain and the part of the brain which inhibits impulsive behaviour does not function as effectively. Toddlers and pre-schoolers are notoriously self-centred so with this in combination, it's a pretty heady mix to cope with.
I found the 123 Magic book the best in terms of teaching a talking toddler how to behave.
Good luck, sit tight, and repeat "This will pass"