I'm encountering opponents that are usually immune at this level. Or, am I missing something simple that can help.
Thanks for your patience with me.
Yes, very effective. Get the perks that make Illusion spells work on higher level enemies---Animage/Kindred Mage for all types of Illusion spells, and then Hypnotic Gaze (for Calm), Aspect of Terror (Fear), and Rage (Frenzy).
Dual casting will more than double the maximum level of enemies/NPCs that your spells can affect.
Fortify Illusion potions will further increase the maximum level of enemies that your Illusion spells can affect.
Take a look here: http://uesp.net/wiki/Skyrim:Illusion and http://uesp.net/wiki/Skyrim:Fortify_Illusion
(Note that Fortify Illusion enchantments only decrease Illusion spell cost; they don't increase the power of Illusion spells).
In addition to this, playing as a Nord or Imperial gives you a very strong innate illusion spell. Fear in the case of the Nords and Calm for the Imperials. Both up to level 99. Very strong stuff, though limited in that they can only be used once a day.