"In an ordinary sense" means according to common understanding. Using your examples: 1) Our souls are not united to our bodies "in the ordinary sense of these terms." = Using the common definitions of the words "soul" and "body", our souls are not united to our bodies. 2) [It is] not a Zoo "in the ordinary sense." = Although this place is called a zoo, it is not like other zoos. It is not a zoo by the common understanding of the word "zoo". 3) It was not sympathy "in the ordinary sense" which he [Adolf Hitler] felt for the disinherited. = Although the word "sympathy" is used to describe what Hitler felt for the disinherited, we don't really mean "sympathy" because it is different from ordinary sympathy. 4) "In the ordinary sense" a police officer is free to ask a person for identification. = It is common understanding (most people would know) that a police officer is free to ask a person for identification. (This isn't true Canada unless the police is able to arrest you by law. Even then, you have the right to silence.) 5) The smallest units of matter are not physical objects "in the ordinary sense;" = The smallest units of matter are not really "physical objects" by common understanding, because they're much smaller so are really "intangible".

It means 'in a normal way' or rather 'in the way you would expect'. 1) "not...in the ordinary sense of these terms" ie. not using normal definitions of 'soul' or 'body (or possibly 'united'). 2) The reason it's defined as a zoo is not the same as normal zoo. 3) It was not the normal kind of sympathy that Hitler felt. ie. his reasons for giving sympathy were different than the normal reason for giving sympathy. 4) This sentence is awkward, it would make much more sense as a sub-clause. As it is, it means "A police officer is ..." with 'in the ordinary sense" stuck on. 5) The smallest units may or may not be defined as physical objects, but if they are they are not defined as physical objects the way most are.