Thank you all for the input.
The kill them then switch the stuff worked...sorta. Now she's walking around without any attire, but if provoked she will put on one of the wigs. Otherwise it seems the game does not recognize the mod clothing.
Using the console command was my first idea, and attempt, but the mod items apparently aren't accessible through the console, until I do something to them in the CS to make them as scarb suggests.
I am downloading the inventory spell and the companion mod, I will try those later today. However just getting the items in the inventory doesn't seem to be enough to get the NPC to equip them as well.
I'm also downloading the Construction set, I've not used it before, so it should be interesting to use. I hope adjusting the reference IDs is as easy as you make them sound. But I'll fiddle with that later as well. Thank you all for the help.
If you use the Active Inventory Spell, they will equip the items. Unless, of course, you give her two items of armor for the same body part, etc., etc., but if you give her a different maid outfit (for instance), she will equip it.
Regarding changing the reference ID's/making copies. This will basically create a new .esp (your own mod) unless you have another active. Let's say you make your own .esp for changing Eyja. You would load up the data for Oblivion and the Goddess mod. You would then find the item from the goddess mod you want her to wear. You double click that, bringing up its information in the CS. At the top there is a section for reference ID. Simply change this to whatever you want (eg dracon001 or whatever). The CS will then prompt you to save a new form since you changed the ID. You select 'yes'. Then find the new item in the list by the new reference number. Then drag this one to Eyja's inventory and delete whatever item is in there you wish to replace.
If you are interested in changing Eyja's appearance and getting even more of out of her and Rosethorn Hall, might I suggest this wonderful mod -
The Romancing of Eyja. This allows you to put many, many difference kinds of clothes in her wardrobe that she will change in and out of depending on the day of the week and the time of day. This also eventually allows her to become a companion of yours, if you so choose to take her along on various outings. It also improves Rosethorn Hall.
If you need any other help or more detailed instructions, please feel free to ask.