In response to the Thebans lamenting and prayers because of the famine and plague, Oedipus sends Creon to the Oracle at Delphi. Creon reports back that the gods have unleashed a plague in reaction to the murder of the previous King Laius (Oedipus' father and Jocastas first husband). If by magical thinking, you mean: finding causation where there may only be correlation or coincidence, then Oedipus links the murder to the state of the kingdom as evidence of growing unrest and crime in the face of famine and plague.
If by magical thinking, you mean having a mental affect or control over nature, then perhaps he is thinking that by finding the murderer, or by solving the kingdom's problems, other problems will fade as well. (This is probably more along the lines of appeasing the Gods, so it's only an indirect way of saying Oedipus believing he can alter the...
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outside world).
There is also the idea of synchronicity, that certain things are synchronic (happening at the same time, and perhaps connected). Oedipus may believe that the murder and plague, famine, etc. are directly related (phenomenally or by the will of the gods); and therefore, if he can rid the kingdom of one problem, the others will go away - not necessarily because they are causally related, but because they are similar: thematically, metonymically, etc.
Does magical thinking allow Oedipus to connect Laius's murder with the kingdom's state?
I think that it might be too strong to label the assembling of information and understanding as "magical thinking." This idea implies that there is a level of consciousness that lies outside of the human domain. I think that the power of Sophocles' characterization is that Oedipus is all too human. Oedipus' plight is not other worldly. Sadly enough, it is of this world. This is what makes Oedipus such a sad and tragic character.
Oedipus does not have to make too much in way of jumps to assemble everything together about his own predicament. The figments and fragments of truth that are given to him from others helps to allow him to understand what is happening and how he is involved. The testimony of other people, the gaps in his own perception of consciousness, as well as the lingering words of Tiresias helps Oedipus to understand everything and gain more insight into how his life connects to what has happened and what will happen. I don't think that this is magic thinking, as much as a rational being able to utilize their own understanding and capacity for thought to be able to gain insight and a sense of vision that transcends the mere physical capacity.