First, the 124- You don't need to oil it. The 124 has a synthetic seal, it doesn't need to be lubricated like a leather seal. You might want to consider giving the 124 a good going over before you shoot it much. The factory seals have a well deserved reputation for decaying into mush. Once that happens you start to get piston slam and damage to the compression chamber. What you need to do is get a quality replacement seal and spring. No sense opening it up to replace the seal and not put in a fresh spring.
The Hw55 most likely has a leather seal. Those seals do need to be kept moisturized with silicone for best performance. Just a drop or two through the port once in a while should do it. If it hasn't been used in years, put in two or three and leave the gun standing for a few days to allow the seal to soak up the oil.
If neither gun has been used for 10 years, you really need to look at the triggers also. When left for extended periods, especially if in a vertical position, lube tends to migrate to the trigger since its at the lowest point. After a while any oil or grease turns to glue and gums up the trigger mechanisms. The HWs Rekord trigger is known for the thick brown goop that was originally grease put there at the factory. The pistons on both guns most likely need a bit of moly lube on them too. If either one ever had lube on the piston, its turned to gunk by how and needs to be cleaned out.
Both guns are very easy to work on as long as you have some sort of spring compressor. Theres really not much in the way of moving parts, the biggest thing is getting the spring out. Once you've done that the rest is easy.
What sort of velocities did you get for each gun?
Look around this site for parts and lubes-
http://www.airguns.citymax.com/page/page/251327.htmJM has the good stuff for both guns. Give him a call and he'll set you up with what you need.
