By and large the easiest way to defeat all three of these enemies are Biotic Combos/Tech Bursts. Try to have a pair of Adepts, with at least one of them being a Drell Adept, in your team of four whenever possible, as the Drell's Reave power (especially when fully upgraded) is invaluable to a team that wants to succeed on harder difficulties. SImply have one of your teammates hit the Banshee, Atlas, or Brute with Warp first, and then follow it up with Reave. Not only will they sustain heavy damage, but they will be prevented from regenerating health while simultaneously being susceptible to more damage.
Another strong alternative is a Krogan sentinel. Put enough points towards his Rage abilities so that he can enter Rage with just two melee kills. This will result in highly increased melee combat damage, and if you can get a charge in on the backs of a Banshee/Atlas/Brute, you can effectively drain two or three bars of their armor, shields, or barrier, making it ideal for a quick kill. Never go for a melee from the front however, it's only putting you in a position to be instakilled.
The fourth position on your team should be filled by an Infiltrator, preferably a Quarian Infiltrator. If outfitted with a sniper (preferably a heavier sniper like the Widow), the Infiltrator can deal a strong amount of damage on these targets while staying a good distance away. Just make sure that your cloaking is upgraded enough to give your Infiltrator the highest possible damage bonus from your sniper headshots, and these fights will be significantly easier. Cloaking can also help if you need to make a quick getaway. I would also recommend fully upgrading her Sticky Grenades. Sticking any of these targets (particularly the Brute) can draing up to three bars of Armor, moreso if your Drell Adept has hit the target with Reave first!
Overall, this team of four should be best suited in taking down any challenges that might rear their heads, and make Banshees, Brutes, and Atlases notably easier than they normally would be. Good luck!