If you are asking for an explanation of the subtle difference in the three words, I think the difference is this:
Your intention refers to the plans you make for the future. If he has no intention to retire, then he has no plans to retire. If he has an intention to keep working, then he has planned to keep working.
Your desire refers to your internal motivation. If I have a desire to keep working, then I feel a passion or internal motivation to keep working.
A wish refers to something that you would like to happen (or not happen). It is not something that you have planned out or that you take action on. It is often something that is out of your control (or something that you don’t want to work hard for ;))!
There is some subtle assumptions that I might make in the examples you gave. If you said Tony has not the least intention of giving up his research work, I would assume that Tony would 'fight' or work very hard to ensure that his research work was not taken away from him. If you say someone has "no intention" of doing something, you might assume they have a fixed or determined mind-set which might be hard to change. Of course, the whole context of what you are saying will colour what assumptions I would make about Tony!!
If you said he had no wish to give up his research work, I might assume that it is out of his control, at least to some extent.
I hope this helps!