Check the last sentence on the card. "Each friendly soldier may only trigger this ability once per round."
So, Double / Triple Strike, Sweeping, and AoE all only trigger it once. There was a point in Development where this wasn't the case, and yes, it was as ridiculous as you're thinking.
[mwcard=FWC04]Goblin Builder[/mwcard] is a Familiar, so you can, yes, put mana on him/her. You can't [mwcard=MW1E20]Harmonize[/mwcard] the goblin because it doesn't have channeling, but that's because of the rules on Harmonize specifically.