It's worth pointing out that all three examples are highly culturally variable.
The "aspie logic" example behaviour is far more common where I live (urban Japan).
In the first, most people lack the facilities to bake, especially young adults in small apartments or dorms. Buying a cake is the obvious thing to do. That or taking the SO to a cake-serving cafe.
In the second, -no one- here holds doors for strangers. I had to train myself out of the habit because it was getting me very strange looks. Similarly, no one says "bless you" or equivalent when strangers sneeze. The rules of courtesy are different.
In the third, it's normal here to expect repeated invitations for any occasion. One invitation will be for show, so you invite people you don't expect to make it as well. The key is that people won't actually make plans to attend until two or more invitations have been received. (This is locally variable; some regions and demographics expect three or four invites. Think of it as a pre-event version of the British quirk where one says "We must do this again sometime" while having no actual desire to repeat the encounter.)
The bottom line is that the other person's expectations ought to be factored into the logic. Beware generalizing from a sample of one and all that.
Followup to: Do you have High-Functioning Asperger's Syndrome?
LW reader Madbadger uses the metaphor of a GPU and a CPU in a desktop system to think about people with Asperger's Syndrome: general intelligence is like a CPU, being universal but only mediocre at any particular task, whereas the "social coprocessor" brainware in a Neurotypical brain is like a GPU: highly specialized but great at what it does. Neurotypical people are like computers with measly Pentium IV processors, but expensive Radeon HD 4890 GPUs. A High-functioning AS person is an Intel Core i7 Extreme Edition - with on-board graphics!
This analogy also covers the spectrum view of social/empathic abilities, you can think about having a weaker social coprocessor than average if you have some of the tendencies of AS but not others. You can even think of your score on the AQ Test as being like the Tom's Hardware Rating of your Coprocessor. (Lower numbers are better!).
If you lack that powerful social coprocessor, what can you do? Well, you'll have to run your social interactions "in software", i.e. explicitly reason through the complex human social game that most people play without ever really understanding. There are several tricks that a High-functioning AS person can use in this situation: