The answer is clear in this FAQ from the ATF: http://www.atf.gov/firearms/curios/1972-2007/faq.pdf
What modifications can be made on C&R firearms without changing their C&R classification?
The definition for curio or relic (“C & R”) firearms found in 27 C.F.R. § 478.11 does not specifically state that a firearm must be in its original condition to be classified as a C&R firearm. However, ATF Ruling 85-10, which discusses the importation of military C&R firearms, notes that they must be in original configuration and adds that a receiver is not a C&R item. Combining this ruling and the definition of C&R firearms, the Firearms Technology Branch (FTB) has concluded that a firearm must be in its original condition to be considered a C&R weapon.
It is also the opinion of FTB, however, that a minor change such as the addition of scope mounts, non-original sights, or sling swivels would not remove a firearm from its original condition. Moreover, we have determined that replacing particular firearms parts with new parts that are made to the original design would also be acceptable—for example, replacing a cracked M1 Grand stock with a new wooden stock of the same design, but replacing the original firearm stock with a plastic stock would change its classification as a C&R item.
See also: ATF letter of interpretation: http://www.atf.gov/firearms/curios/1972-2007/faq.pdf
This letter of interpretation also may be of great interest: http://www.surplusrifleforum.com/vie...p?f=39&t=47212
I encourage everyone to do their own research on legal questions and use "source documentation" to obtain their legal opinions - people can be, and often are wrong...even me. And if in doubt, always contact ATF for a written interpretation of your own specific issue.
Reference the original posters questions:
1. Regarding your Mosin Nagant Rifle. It would lose it's C&R status if you put a Monte Carlo or any type synthetic stock on it. If you replaced it with a similar designed stock (like another wooden one from another Mosin Nagant) it would not lose it's C&R status.
2. Regarding the C&R status of the SKS. Yes, most SKS's are C&R (Chinese are not). Read here and double check: http://www.atf.gov/firearms/curios/index.htm
3. Reference your stock question for your SKS. It would lose it's C&R status if you put a contemporary folding stock or collapsible stock on it; however in addition since the SKS is a semi-auto firearm it would remove it as a Curio & Relic and place it as a non-sporting firearm - and thus, you need to play the parts game under 922(r).