Is pedophilia a sexual orientation or a mental disorder? There are some different claims being made that pedophilia is a sexual orientation rather than a mental disorder.

At the moment there seems to be a growing group of psychologists advocating that pedophilia is, or at least should be considered a sexual orientation rather than a mental disorder.

For example:


  GOOD: You're a member of a growing group of psychologists who say
  pedophilia should be considered a sexual orientation. Why?
  
  Quinsey: Part of the definition of pedophilia is a person has a
  preference for a particular kind of partner. [...] pedophiles,
  unlike other men, show substantial sexual interest in prepubescent
  children. As far as we know—and many people have tried—these sexual
  interests are not modifiable by any method that’s been tried yet. So
  it appears like pedophilia is a sexual orientation. [...] You also can’t modify that
  interest; it’s stable through adulthood, just like pedophilia.


Another example:


  “Pedophiles are not simply people who commit a small offence from time
  to time but rather are grappling with what is equivalent to a sexual
  orientation just like another individual may be grappling with
  heterosexuality or even homosexuality,” emphasized Van Gijseghem.
  
  “True pedophiles have an exclusive preference for children, which is
  the same as having a sexual orientation.  You cannot change this
  person’s sexual orientation.” He added, however: “He may however
  remain abstinent.”


There is also an advocacy/support group for people attracted to minors, B4UACT, who state in a section from their website (emphasis mine):


  Why do you say that minor-attracted people are stereotyped?
  
  Popular beliefs about minor-attracted people are not supported by the
  evidence. Research shows that they are no more violent or aggressive
  than the general population, nor do they suffer from psychopathology
  or personality disorders. As a group, they do not share any particular
  characteristics or behaviors other than their feelings of attraction.


As I understand things mental disorders tend to have observable associated symptoms, while a sexual orientation would not as it is just an instinctive attraction (in the general sense of the term).

Are there studies that suggest that pedophilia is a sexual orientation? Do traits typically associated with a mental disorder apply to pedophilia?
Before trying to give any sort of answer, it is important to address a common misconception. In popular culture, the terms child-molester and pedophile are often equated. Scientifically, they are not at all the same. The approximate scientific definition for a pedophile is:


  an individual that has an unwavering sexual attraction to prepubescent children similar to attraction heterosexual men have for women


This means that a pedophile might or might not molest children, and a child-molester might or might not be a pedophile. Further, implicit in this definition is a close resemblance to a sexual orientation, and if you want a through and careful discussion of this (much better than my answer) then read:


  Seto, M.C (2012) Is Pedophilia a Sexual Orientation? Archives of Sexual Behavior 41(1): 231-236.


Now, the actually relevant scientific discussion (as opposed to merely a semantic distinction) is threefold: (1) can pedophilia be considered a choice in the legal sense? (2) what causes it? (3) can it be treated?

Note that for what we typically consider sexual orientations, questions (1) and (3) have clear answers: no, and no. However, for mental disorders, all permutations of answers to (1) and (3) are possible. Thus, answering these questions does not let you clear up semantic ambiguity.

To start with question (2): in broad strokes Blanchard, et al. (1999) and Cantor, et al. (2004) suggest that pedophilia has a prenatal cause. For question (3) there has been no evidence to suggest that pedophilia can be treated or "cured", much like how you cannot "cure" homosexuality. This lead to Van Gijseghem expert testimony before the Canadian Parliment's Standing Committee on Justice and Human Rights that you quote from in your question. He concludes that pedophilia cannot be 'cured' through penal intervention. However, it is possible for a pedophile to abstain from becoming a child-molester. 

This leaves us question (1), the legal part of this. In Canada, being a pedophile is not a crime, but molesting children is a crime. The status of pedophilia as a mental disorder or sexual orientation is irrelevant to this since both mental status and sexual orientation are protected by Canadian law as long as they do not infringe on other's rights.  To help pedophiles abstain from molesting children there is the Circles of Support and Accountability (CoSA) program (note: it deals with all kinds of sexual offenders, not just child-molesters). This program is aimed to manage and not 'cure'. Wilson et al. (2007, 2009) have shown that CoSA produces dramatic decrease in re-offence rates for sexual offenders.