As promised, Striker's next.

Here's a true Punchbro build. This may be slightly shorter, but it's still gonna be a lot of words.

• Flashbang Grenade: Completely shuts down enemies hit by it, and has a deceptively large blast radius. Also both other options are AoE type grenades, so screw those. But again, you should try out all three and find what works best.
• Catapult: As with Defender. Personal preference, find the one you like best.
• Shockwave: This increases the effective range/area of Fist of Havoc quite a bit. Aftermath is another AoE, so nope. Death from Above I honestly never got the hang of. I hear it's useful, but more for PvP than PvE, but takes a bunch of practice. If you are good with it, feel free to use it, I'm not.
• Discharge: Splash damage on melee is quite nice. Overload is RNG based, as if there wasn't enough of this in the game already. Amplify is a fully viable alternative, and may even be stronger by some measure. This one's really preference, use whatever you like better.
• Titan Codices II and VI: This is a close combat build, so we want lots of Agility to get in fast. And of course Armor to be tough as well.
• Transfusion: A bit of a key point of the build, as healing off melee is great. Esp because it works for Shoulder Charge as well. Headstrong is decent, and gives a point of Agility, but it's just outclassed. Aftershocks only applies to AoE effects, so I'll pass.
• Shoulder Charge: Only real choice for a melee/Transfusion build. Unstoppable is okay, but only has a real use in PvP, and even there is rarely truly necessary. Juggernaut is good too, but the goal of the build is as much melee as possible, so we use the offensive option.

Playstyle: Get in there and punch/Shotgun all the things. Transfusion allows you to regain health off melee kills as well. Shoulder Charge takes a bit of getting used to to get the window of activation right, but if you keep using it, you'll quickly get it.
Armor: All the subclass-neutral ones are decent here as well. Striker-specific ones are Insurmountable Skullfort, Helm of Inmost Light and Mk.44 Stand Asides. Inmost Light is pretty much only a PvP helmet, and I don't do much PvP, so I have little to say on that one. Stand Asides are bad, and they should feel bad. Really not worth the exotic slot. Ever. The Skullfort is easily the best choice. Regardless of what the description says, it simply grants the Transfusion perk, freeing up the slot on your subclass for Headstrong (really mostly the +1 Agility).
Weapons: Close quarters. Shotguns, Fusions, stuff that can be hipfired or has low zoom. Of note: Monte Carlo, as on any melee build; Red Death, it got buffed big time, and gives you some more health restoration; Fang of Ir Yut, a legendary, and I just really like this one, plus it's a great long range option; Invective, because Full Auto and ammo regen; Swordbreaker and Murmur both for Grenadier and good stats. As usual, find some stuff you're good with and use that.

As it turns out I use Defender way more often, and thus only have this one Striker build to offer. I think a build of this type would be possible, going a support role with maximum toughness and area denial, but no guarantees this spec would really work, it's just some theory-crafting I came up with on the fly.

Hope this helps you out some, if there's anything else feel free to ask.