Meaning of "they inflicted serious injuries on three other men".
I understood like this "they beated three persons".
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It means they caused injuries to them. It doesn't say how. They may have beat them, hit them with a car, stabbed them, or something else. All we know is that there are injuries, and they aren't just light bruises.
A serious injury is normally something you have to go to the hospital for. The image that is conveyed is someone getting stitches for a laceration, but it could mean broken bones, serious bruises, a concussion, or something like a lost limb. Whatever the injuries are, it will be some time before a full recovery is made and likely there will be permanent effects.