I have a single 4mm stranded wire I want to connect to 3 x 2.5mm solid wires. At the moment I've simply wound them around each other temporarily and sealed with electrical tape - but how is it done securely?
Is this for AC wiring (more permanent house wiring, that needs to meet code, or for something else?
If I were you, I would look into wire nuts, they may be able to get it done the cheapest/most effective.
Also check out the splices used in this question about grounding Grounding wires
Alway trun off the power.
I use Klein Linemans/Pliers to twist the solid wires together, making sure that all the plastic covering of the wires line up. Next I strip the stranded wire, a little longer then the solid wire, and that the plastic covering of the wire lines up and twist the stranded wire around the solid wire with the pliers. Next using the plier I cut the tip of the new bundle wires, making sure to cut all of the wires, making a good bond. Lastly I wire nut them all together and pull on the stranded wire to make sure that is under the wire nut and does not come out. If the stranded comes out, repeat proccess until it is all secure under the wire nut. No copper should be showing once the wire nut is installed.
You can buy connectors made specifically to join stranded and unstranded wires
For example Wago lighting connectors
can be used in nearly all electrical connections where a connection between solid and fine-stranded conductors is required for household and similar purposes in buildings. Applications can be, for example, automated blinds or awnings, window or bathroom fans, boiler controller, tight connections of electrical devices with stranded conductors, circulating pumps etc.
There are also lever-action clamping connectors that allow solid, stranded and fine-stranded wires to be connected:
For example Wago 221 series
Other connector manufacturers exist.