Here are the original types I proposed last January.
Type 1 - "Limited Intangibility" - refers to characters whose bodies are composed of an immaterial or energy substance (eg, fire or light), which recovers its shape in the event it is damaged. This intangibility can be overcome by opposing elements or (often) using special abilities. Also this level is vulnerable to certain effects such as sound, gravity but direct physical contact can be ignored due to unspecified levels of Regenerationn. However, this level of intangibility does not have the ability to pass through solid objects.
Note: Cal said he preferred if this was called "Fluid Intangibility instead."
Examples of characters with this type: Logia users, Kabuto Yakushi
Type 2 - "Intangibility via existing in a different dimension" - refers to characters whose body is entirely or partly transferred to another dimension / plane / reality that allows them to ignore some of the effects of the ordinary world. There may be attacked by dimensional manipulation or those powers that continue to apply to them (sound or gravity). Attacks using the properties of similar abilities also affect such a being in partial transition.
Examples of characters with this type: Obito Uchiha
Type 3 - "Intangibility via energetic existence" - refers to the characters that exist in the form of intangible energy (for example, soul, quantum foam, magical form, or just particles that do not have clear links between them, and are able to pass through solid material). They can ignore almost any exposure, excluding special abilities that relate to them (a soul wouldn't be able to ignore soul manipulation for example.)
Examples of characters with such abilities: Sasaki Kojiro (in astral form), Michael Roa Valdamjong (in between reincarnations), Post Retcon Beyonder (Cosmic Cube)
Type 4 - "Intangibility via Abstraction" - refers to those characters who are completely devoid of any specific material or energy, such as existing in the form of information or aspects of reality itself. These beings are immune to any effects other than the reality warping and cosmic powers. It is worth noting that such creatures still are part of the normal dimensional universes and timelines and therefore are not immune to the effects of higher-dimensional beings.
Examples of chatacters with this type: Phoenix Force, The Endless, the Living Tribunal
Type 5 - "Intangibility via Meta-abstraction" - refers to meta abstract characters, which among other things, are independent of the concepts of space, time and dimensions, or the reality of multi-layered universes. They possess an intangible immunity to even reality warping on the levels of the dimensional universe, and they are vulnerable only to effects from the same level or higher existence.
Examples of characters with this type: the Chousin, Nyarlathotep (Demonbane), Kawahara Sakuya