Additional Topic: How to Use Dee Jay's Hyperfist in USF4 (AKA How to Machine Gun Punch Without a Machine Gun)
Dee Jay's Hyperfist punch maneuver is a multi-hitting attack which is actually Dee Jay's most damaging basic special move. Despite this, you are not likely to see it as much as his other moves because of the nagging limitations it has - it requires a down charge, has a tendency to miss or be blocked after a few hits (making it more difficult to hit confirm), it sometimes is wonky when used against certain characters, and, to top it all off, is unsafe on block now. These properties mean that the only time you will see the Hyperfist is in a combo where the situation allows it to hit fully.The three different versions differ mostly in damage, with the heavier Machine Gun Uppers doing considerably more than the lighter ones (they're great for building Super meter, too). You can mash buttons to increase the damage slightly, although the damage and dizzy factor this move had in SF2 Super Turbo are completely gone. Of all of Dee Jay's regular specials, his Hyperfist is the least noteworthy of the bunch, being restricted to combos that must be landed in different ways, depending on the character (see my combo reference sheet as well as the updated combo gems near the end of my joystick mechanics post for a rundown of these).
Other than its damage factor and combo potential, the humble Hyperfist doesn't have much to offer.
TLDR: Use the normal version of the Hyperfist primarily for combos. Use the EX version to put teeth in your combos and get throw-crazy opponents off your back.
NOTE ON EX VERSION OF HYPER FIST: The only really potent version of the Hyperfist is the EX version which not only allows you to mash and get more damage than a regular Hyperfist, it also allows you to juggle with an assortment of Dee Jay's moves (including his neutral Jump Fierce, standing close Roundhouse for one hit, Upkicks, EX Dread Kick, and perhaps most impressively, his Ultra 2).
While the EX version does not have enough invincibility to regular attacks to make it useful as a consistent reversal, it IS throw invincible during the early parts of its animation. For this reason, my two main uses of the move are either as part of a heavy-hitting combo or as a punishing counter to an opponent's walk-in throw attempt. Landing this on an opponent going for a throw and then following up with a heavy damage follow-up will certainly make them think twice about attempting a throw again.
2024 UPDATE: Dee Jay's EX Upper also has some useful applications for footsie play which you can read about here.