Many words and phrases originate in technical jargon, where they had meanings specific to the relevant field; later, they are often popularized in regular language, where their meaning changes into something more general, less specific to the field. We may then say that such an expression is used either technically/narrowly/strictly or broadly/generally/popularly.
Kate Moss is really obese: Chanel
won't hire her any more. I mean, she
isn't technically obese, since her
Body Mass Index, the number doctors
use to determine obesity, is still
quite low; but that doesn't matter on
Since technical jargon is often more precise and detailed than other language, the phrase technically [speaking] is tending to develop a meaning identical to strictly speaking, as in your example. This in turn may sometimes even evolve into something closer to a general intensifier, like really.
This broader use of technically is resisted by some, who feel that it introduces another synonym of strictly that we hardly need, while rendering its original sense, as used in the relevant field, unusable. They advise that technically be reserved for expressions used in a sense specific to a certain field or profession, as opposed to cases where strictly would do.
Literally means non-figuratively, non-metaphorically: if you mean something literally, you say it in such a way as to exclude anything but the simple interpretation, if several interpretations are possible.
I am literally burdened by my large breasts: their weight hurts my back. I am also figuratively/non-literally burdened, because I don't feel free to wear any shirt I like because of them.
This word too is now often used to mean something like strictly speaking, and even as a general intensifier, which is strongly discouraged by many style guides.