Hey there, not necessarily my area of expertise, but I'll take a shot at it (no pun intended). One of the key problems with studying the Huns style of warfare is that it's not very well recorded. All our records of the Huns, as far as I know, come almost exclusively from their enemies, such as Jordanes and Marcellinus, which often leads to over-exaggerations, inaccuracies, and plain old fashioned bias in accounts. It also means that there's not an excessive amount of focus devoted to the actual warcraft of the Huns. We know some hallmarks of their strategy: Lots of horse archers (almost to the point of exclusively horse archers), divided into regiments/warbands along familial lines, operating in a single battle line at a distance focusing primarily on hit-and-run and feigned retreat into ambush tactics. In practice, the Huns would attempt to disrupt enemy formations with arrow fire and maneuver, drawing them out into a more unruly group, then move into to close down on the disparate forces once they were overextended and vulnerable. The following is more speculation my part, but I would imagine this was the stage where the majority of the killing was actually done. The arrow fire at a distance was not so much meant to wholly slaughter the enemy as it was meant to force them out of rigid formation, tire them out, demoralize them, and generally make them break, at which point the Huns could move in and just clean up. That would generally be in line with Marcellinus' description of their tactics and probably answers your question regarding the fact that their arrows were supposedly not able to reliably pierce Roman infantry armor. They didn't need to consistently pierce, because the actual killing came in the form of saber-work after the enemy was broken and/or overextended.

As far as grand strategy (i.e. outside the tactical level), the Huns under Atilla were more about bluff, maneuver, and raiding then they were about actually engaging in pitched battles with Rome. With their ability to move quickly, Atilla was able to choose his battles readily, and really engaged with the Romans only when it was absolutely necessary to do so. If his aims could be reached through threats and belligerence, then that was a far better outcome. If raiding and harrowing achieved his aims, that was also usually preferred to actual engagement. Atilla's campaign in Italy, for example, was essentially just raiding and occasionally skirmishing with Roman forces, trying to pin them back into a position from which he could coerce them into giving in to his demands. As such, the Huns were very happy to engage in sieges to extort what they wanted (or just take it, they were surprisingly good at sieges it seems). Additionally, Atilla made significant use of local forces to bolster his own armies, especially in terms of infantry for pitched battles. The Huns rarely entered into a pitched battle alone, they almost always brought local auxiliaries to fight on their behalf. At the Catalaunian Plains, pretty much the most iconic pitched battle of Atilla's career, the Huns fought alongside numerous local tribes, including the Franks, Thuringians, Burgundians, and Amals (who would eventually become the Ostrogoths). In that particular case, these allies were left to hold the flanks, freeing up Atilla's trusted Hun troops to engage with the center of the enemy line. Again though, at the Catalaunian Plains, we see a demonstration of why the Huns were hesitant to engage in pitched battle, because their raiding/retreating tactics seemingly fail and they were not able to go toe to toe with heavy infantry and/or heavy cavalry formations in order to take the crucial objective of the ridge.

So, in summary, the grand strategy of Atilla the Hun was:

A. Selective engagements, taking full advantage of superior mobility, preferring raids and sieges to pitched battles with Roman forces. They struggled in pitched battles and Atilla was seemingly aware of that.

B. Use of threat and performative violence to force agreements and/or coerce enemies into meeting his demands. After you wholesale slaughter a couple of towns that didn't surrender to your demands, it turns out people are a lot more likely to give you what you want.

C. Incorporating local allies to multiply force and fulfill roles the Huns typically did not perform well in, namely as infantry and heavy cavalry.

Sources

The World of the Huns: Studies in Their History and Culture - Otto J. Maenchen-Helfen

The Roman History Ammianus Marcellinus - Ammianus Marcellinus

The Huns and the End of the Roman Empire in Western Europe - Peter Heather