My question is what is irimi? Does that describe any other entering motion towards the uke that is NOT tenkan? It looks like there is multiple positions that irimi can take - none of them are consistant like tenkan.   

Irimi is a method of entering an attack, as is tenkan. The best way to understand irimi and tenkan is to know that they are both methods of entering an attack for the best advantage. These two differ in the ways they undertake their tasks.

First, in Aikido if you observe very carefully please notice that in all practice we are always "setting-up" ourselves for the most advantageous positioning. This goes on from the very start through the entire technique and then lastly to the pin.*  In Irimi and Tenkan, we are doing just this.

In typical Irimi, we approach the attacker more directly by approaching his front, or rather to his inside. Primarily, we slide at an angle towards the assailant. This angle can vary depending upon the technique we are performing and other small variables. Basically, we can vary the irimi positioning to fit the need at hand. Sometimes we need to slide in deeply, or drop our body lower when we enter, etc. In nearly all cases, it is practiced as a single movement before the execution of the actual technique (such as Shihonage or Sokumen - Iriminage). The work involved in the irimi entrance is getting your best positioning during the attack. This is not easy.

Tenkan is an entrance to the attacker that involves a step to the outside of his body and 180° turn and stepping back once again. The difficulty in positioning here is that you need to be constantly aware where your positioning is in relationship to the attacker. Being that both persons should always be moving during the technique – getting the best positioning for the technique takes time to master.

Sometimes, in execution - I will vary the tenkan. During shihonage I will need to turn sharply towards the uke at the very end of the execution because he is so very tall or physically bulky --- that I need the extra extended movement to keep him off balance. This tenkan too, is a single movement to get the better positioning and advantage.

William Gleason, 6^th Dan of Boston, MA., during a seminar mentioned that irimi is attacking the opponent’s attack more directly and that tenkan is an approach that we take when we are attacking around the attacker. (The idea that when we defend --- we are actually attacking an attack is a widely accepted idea in martial arts.)

I am currently working on some animated GIFs to illustrate a few variations of irimi and tenkan, in actual techniques. Please expect these out sometime in the summer months.