I can still see some people wondering how it's done. It's actually simple but easily missed.
Below you can see that my Venomancer have all the immortal effects even though I am wearing non immortal items. First, you need to have the immortal items in your dota 2, then just equip the non immortal items you like. Notice the skill icons which i have already highlighted, you can actually click on them and a drop box will appear, just choose the immortal item for the effects.
You're welcome.
PS. Does not work the other way round. Also, post game will always show the immortal items equipped – just ignore, your hero loadout is still the same.
Source: https://www.reddit.com/r/DotA2/comments/zqtx2v/for_those_still_wondering_how_to_use_immortal/