I've solder for pushing well over 50 years now. The one thing you have to do is have totally clean wires to solder. If you are trying to solder dark looking older wires, they will not solder until they are clean and shiny copper, or tinned colored wires. And if those wires are dark all the way down under the insulation, you can use a vinegar and salt solution to clean the wires (replacing that wire is a good idea as well). It takes mere seconds to clean older wire to good copper again. Then rinse them in a baking soda solution and water and they will solder with ease.
The second is a quality soldering equipment. I use a Weller WE51 station for a lot of reasons. But it has never left me down. It has the capabilities to change the heat ranges for different applications as well as different type tips. I usually go about 600 to 650 degrees and leave it there. It works with all types and diameters of solder I use.
Also, DO use soldering flux when soldering! The flux, when heated, cleans the wires as it heats up and will accept solder quicker then not using it. Regardless what solder you use (60/40, 63/37 etc.), even solder that is suppose to have a flex core, use a quality liquid flux. If you are experienced soldering copper pipe, you know what the flux does. It does the same for soldering wires as well. If it takes you more then 10 seconds to get the solder to melt and flow, there is something wrong. Most of the time, I can solder wires and/or circuit board connections in mere 2 to 3 seconds. So with the proper cleaning, flux, heat and temperature, you should be able to solder most anything you come across...except copper pipes. Also keep your soldering tip clean and shiny with solder on it at all times. I usually wipe the tip across a wet slotted sponge before each solder connection for two reasons. First it cleans off the corrosion that gets on the tip between soldering events. Yes it happens that quick. Secondly it makes the tip just a little cooler and therefore cycling the heating element on to allow the heat to build as you solder.
As you get ready to solder a connection, apply a little liquid flux to the connection first, then apply the tip of the soldering pencil tip to the wire and add the solder right at the tip where it meets the wire. That will help transfer the heat and melt the solder the quickest. And that IS how it is taught when taking NASA certification soldering courses.
Try these things and get back with us. I think you will be pleasantly surprised how easy and quick you can solder then. If you need more assistance, come back and let us know. JMHO