Having found myself unable to sleep at 6:00AM, I've decided to briefly visit the subject of firearm oils. Now, firearm oils are a subject as old as firearms themselves, and one that has led to an enormous amount of debate and discourse.
Depending on the type of firearm, operation mechanism, and rate of fire, you'd want to pick the right oil for the job. Now, I'm by no means an expert on the subject - frankly, I consider myself barely a hobbyist. With that being said, I do want to say - as I typically only have the space for a break-action single-shot rifle (typically a .22), I tend to go with a heavier-weight grease for my rifle's folding mechanism.
Whenever I purchase a new firearm, I typically disassemble the entire rifle, including the full mechanism (as opposed to a simple field strip). With a handfile, I like to go through and clean up any poorly-manufactured components. As I'm fond of buying lower-grade firearms, I find that many of them have quality control issues - metal shavings, unburnished edges, burrs, and poorly-drilled holes.
So, I'll go in with a manual drill, a handfile, and a bit of sandpaper, to ensure that the gun's fit and finish is excellent. Once that's done, I like to use a very heavy grease - typically, petroleum jelly - as I keep my rifles in an incredibly humid environment - occasionally, with direct water exposure.
While thin oil is better for operation, thick oil tends to fare better with dust - sand and hard, fine materials tend to turn thin oils into a cutting sludge - whereas grease tends to prevent excessive wear with a dirty firearm. This is how I store my guns - I always coat my firearms with a thin layer of gun oil, but, when gun oil is unavailable, I opt for a thin machine oil - sewing machine, or typewriter, will suffice.
In the absolute worst case scenario, motor oil may be used - conventional is preferable to synthetic, as the additives may interact with the firearm's finish - particularly for wood-stocked rifles. For automatic firearms, or rapidly-cycling semiautomatic rifles and pistols, I recommend a thinner gun oil. A medium-thickness oil works best for bolt-action, lever-action, and most slow-cycling semi-automatic rifles.
Now, the following may be slightly controversial - I use cutting board oil on my wooden stocks. Boiled linseed or tung oil is the typical option, but my formulation contains mineral oil. Personally, I like the finish cutting board oil (a formulation of mineral and a few food-grade additives.)
As I like to sleep with my rifle (unloaded and barrel-cleared, of course - solely to hug), I find the mineral oil to be inoffensive in odour, and stain the bedsheets less. Though, I cannot recall the last time I've had a wood-stocked firearm, for plastic stocks, I like to use a thin application of mink oil, to restore the plasticizers; ensure you leave a thin layer, and then wipe off any excess.
I will mention - beware of polymerization - the same effect that you want on the surface of your cast iron pan is the *last* thing you want inside your trigger; sure, firing will burn off most of the oil within the barrel and breech, but, I don't know a single occasional shooter (myself included) that disassembles their entire mechanism after *every* shooting session.
Oil + Heat + Time (even post-cooling) = GUNK
Excess application of oil to plastics will cause elements to degrade, and become sticky. Ensure you aren't applying oil to rubberized elements - some rubbers are resistant to nonpolar substances, but, at times, especially with off-brand rifles, it can be difficult to determine the exact composition of a rubber stock. I can personally assure you there is nothing worse than a sticky rubberized grip - be it your screwdrivers or your favorite gun.
Just you wait until I tell you that I use isopropanol for cleaning my barrels instead of a dedicated gun solvent. ;)