It seems to me that you're mostly asking about star naming conventions, which is unfortunately a difficult thing to master because there are many many conventions. What makes this process difficult is that the conventions you seem to be referencing don't come from Hipparcos at all. Likely you're seeing the names of these stars as they're referred to by some other, more popular convention. I'll try to go through the things you have listed and describe how those conventions work.
Hipparcos Names
A star in the Hipparcos catalogue is given a number. That number is preceded by HIP and you cite a good example of HIP 36623. The number itself is more or less meaningless for the star. Some catalogues provide numbers to stars based on their RA and/or Dec, but for the Hipparcos catalogue the number is the same as the that in the Hipparcos Input Catalog (all HIP stars were pre-chosen for observation and defined in an Input Catalog). The star entries are, with a few exceptions, ordered by increasing HIP number, which basically follows the order of the object's right ascension (Equinox J2000) independent of declination.
You can find a pretty good list of Hipparcos variable conventions on this page.
Bayer Convention
You also cite the names Delta Orionis and Omicron Puppis. These names come from the Bayer naming convention. The general scheme for this convention is to group stars by the constellation they're in. Then you rank all of them by brightness. You give each star a name which includes a Greek letter then the Latin name of the constellation it exists in. The brightest star is alpha (equivalent to A), the next brightest beta (equivalent to B), then gamma (equivalent to C), and so on. There is a convention about what to do once you've run out of Greek letters, but honestly, I've never seen anyone use the Bayer convention for such stars. It's generally only used for the brightest stars in a constellation.
From the examples you gave, Delta Orionis is the 4th brightest star in the Orion Constellation (since delta is the fourth letter in the Greek alphabet). For Omicron Puppis, that's the 15th brightest star in the Puppis constellation. In this convention, you can sometimes see the greek letter written as a Greek letter, rather than spelled out, and occasionally the constellation name is shortened. Thus, for your examples, you might see them written as $\mathrm{\delta}$ Ori and $\mathrm{\omicron}$ Pup. Note that lower-case Greek letters are used (first), not upper case.
Variable Star Type Designations
Variable stars are complex and come in many many different flavors. As such, there's a whole slew of different names and schemes to be used when referring to a variable star. A good reference site is the International Variable Star Index page. You can refer here to answer most of your questions, but I'll post the descriptions of the non-alphabetic characters.
A pipe character ( $|$ ) between two different types signifies a logical OR; the classification is uncertain and all possible types are indicated. An example of this is ELL|DSCT, where the star may be an ellipsoidal binary system or a DSCT-type pulsating variable with half the given period.
A plus character ( $+$ ) signifies a logical AND; two different variability types are seen in the same star or system. An example of this would be ELL+DSCT, where one of the components of an ellipsoidal binary system is a DSCT-type pulsating variable.
A slash character ( $/$ ) indicates a subtype. In the case of binary systems (eclipsing, ellipsoidal or reflection variables) it is used to help describe either the physical properties of the system (E/PN or EA/RS), the luminosity class of the components (EA/DM), or the degree of filling of their inner Roche lobes (EA/SD). This is the GCVS classification system. In cataclysmic variables, slash characters are used to indicate some properties of the system, as in the degree of polarization (NA/DQ) or the nature of their components (UG/IBWD).
This site doesn't specifically indicate the meaning of the colon, but research elsewhere indicates that the colon is used to "indicate the uncertain nature of the classification". It looks to me that within variable star designations, and particularly by the General Catalogue of Variable Stars, a colon used anywhere (not just on the variable type designation) implies uncertainty.
