How to answer questions that don't seem to be possible to be answered on a Strongly disagree - Strongly agree scale and what's their point?
Really good question - I've had this exact conversation with a student.

It's important to understand that mature scales are validated:


  In the fields of psychological testing and educational testing,
  "validity refers to the degree to which evidence and theory support
  the interpretations of test scores entailed by proposed uses of
  tests".


An interesting example is predictive validity:


  ... the extent to which a score on a scale or test predicts scores on
  some criterion measure. ... predictive validity provides somewhat more
  useful data about test validity because it has greater fidelity to the
  real situation in which the test will be used. After all, most tests
  are administered to find out something about future behavior.


From the point of view of the developer of a psychometric test, what a subject might think of a question, how they interpret (or misinterpret) it, or what ambiguity it contains, is not as important as whether or not answers to the question contribute to the validity (especially predictive validity) of the test.  A question that seems meaningless to you, might actually be highly predictive (at least in general) of the criterion measure.

It is not always necessary for the developer to know why a question is predictive, only that it is predictive (provided other validation criteria are also met).  Scales in general are developed using the scientific method - a survey you take that contains say, 20 questions, might originally have contained over 100 questions.  After testing the scale on an experimental group, researchers may discover that 20 of those questions provide 80-90% of the predictive power of the full test, and decide to shorten it.  Researchers cannot really know in advance which questions work best - that's what testing is for!

Another interesting factor in psychometric testing is demand characteristics:


  In research—particularly psychology—demand characteristics refers to
  an experimental artifact where participants form an interpretation of
  the experiment's purpose and unconsciously change their behavior to
  fit that interpretation. ... A possible reason for demand
  characteristics is the participant's expectation that he or she will
  somehow be evaluated and thus figures out a way to 'beat' the
  experiment to attain good scores in the alleged evaluation.


In other words, if you feel like your test score forms some evaluation of your character, then you might try to provide answers that you think will form a desirable evaluation, rather than an accurate one.

However, it is difficult to ascertain the value or purpose of a question in a test - some scales contain questions added for testing internal validity, specifically for detecting demand characteristics and other biases that may affect results.  For example, a test may contain 2 identical questions worded differently.  Different responses to these questions could indicate dishonesty, misinterpretation, inconsistency, or inattentiveness.  Bottom line: I wouldn't worry about what the point of a question is - don't over-think it.