Larfleeze use Infinity Gauntlet.
So, construct token can use all effects the Infinity Gauntlet powers and abilities in close combat purposes?

No. (filler)

Please quote the game effects in question:

Orange Constructs: Orange Construct objects are objects that can't be picked up and are removed from the game if Larfleeze is KO'd. Whenever Larfleeze is moved, after actions resolve you may move any or all Orange Construct objects an equal amount. Larfleeze considers characters adjacent to or in the same square as an Orange Construct object to be adjacent to Larfleeze for Poison and close combat purposes.

So the Orange Constructs never actually do anything. All that happens is Larfleeze can act through the constructs for Poison and close combat. So if Larfleeze can suddenly use BCF or CCE or something similarly close combat-ish via the IG, he can use it through a construct.

lol

The tokens can not use anything. Larfleeze can use the Gauntlet. He can considers characters adjacent to his constructs adjacent to himself for close combat and poison:

ORANGE CONSTRUCTS: Orange Construct objects are objects that can't be picked up and are removed from the game if Larfleeze is KO'd. Whenever Larfleeze is moved, after actions resolve you may move any or all Orange Construct objects an equal amount. Larfleeze considers characters adjacent to or in the same square as an Orange Construct object to be adjacent to Larfleeze for Poison and close combat purposes.

So powers that he can use through the Gauntlet for close combat purposes (i.e., Quake, Close Combat Expert, Flurry, etc), could be used "through" the tokens.

I've done this once, and it was A LOT of fun. Larfleeze is generally tough to play, but the Gauntlet makes him very viable and a blast to play.

In APOTHEOSIS APPROACHING and ULTIMATE GODHOOD ATTAINED special power the IG say: choose a standard power character can't already use.

So I choose HSS. How this works in Larfleeze construct tokens?

Give him a power action to use HSS. Use HSS normally, except if you have him make a close combat attack, you can make that attack against an opposing character adjacent to one of his Orange Construct objects. Then, after the action resolves, you may move any or all Orange Construct objects an equal amount.