I’ve Linux Mint 19 with over 10 versions of erlang and elixir installed via asdf without any problems:
alexiss@alexiss:/work/home/alexiss$ asdf list erlang
20.0
20.1
20.2.2
20.2.3
20.3.1
20.3.2
21.0.8
21.1.1
21.2.1
21.3.2
21.3.6
21.3.8
22.0.1
alexiss@alexiss:/work/home/alexiss$ asdf list elixir
1.5.1
1.5.2
1.6.1
1.6.4
1.7.2
1.7.3
1.7.4
1.8.1
1.8.2
alexiss@alexiss:/work/home/alexiss$
Try to install it step-by-step following links from this post
Also make sure you complete all steps for Ubuntu before installing erlang