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His Phoenix Blade is a flaming halberd that inflicts D3 wounds vs enemies with a unit strength of 2+

Does that mean he can do between 3 to 6 wounds VS a fully ranked unit? Or only multi-wound models?

"All attacks made with the Phoenix blade are flaming attacks. In addition, it causes not one but D3 wounds against enemy models with Unit Strength 2 or greater"

Only multi-wound models.

As a general rule wound multiplying such as this only effects multi wound models or single wound models in a challenge (for the purposes of overkill). This is listed in the Rulebook under wound multiplying.