Switch Audio Outputs from CLI in Ubuntu

Thanks to the discussion with @Thomas I realised the proper therms (key words) are profile and card. In the terms of the question profiles are the inputs and outputs. The cards are the audio devices. And the sink numbers are not so important, but we need them.

We can find all available profiles for each card name by the command pacmd list-cards or pactl list cards that outputs the same information:

$ pactl list cards

Card #0
    Name: alsa_card.pci-0000_00_1b.0
    ...
    Profiles:
        input:analog-stereo: Analog Stereo Input (sinks: 0, sources: 1, priority: 60, available: yes)
        output:analog-stereo: Analog Stereo Output (sinks: 1, sources: 0, priority: 6000, available: yes)
        output:analog-stereo+input:analog-stereo: Analog Stereo Duplex (sinks: 1, sources: 1, priority: 6060, available: yes)
        output:analog-surround-21: Analog Surround 2.1 Output (sinks: 1, sources: 0, priority: 800, available: yes)
        ...
    Active Profile: output:iec958-stereo+input:analog-stereo
    ...

Card #1
    Name: alsa_card.pci-0000_03_00.1
    ...
    Profiles:
        output:hdmi-stereo: Digital Stereo (HDMI) Output (sinks: 1, sources: 0, priority: 5400, available: yes)
        output:hdmi-stereo-extra1: Digital Stereo (HDMI 2) Output (sinks: 1, sources: 0, priority: 5200, available: yes)
        output:hdmi-surround-extra1: Digital Surround 5.1 (HDMI 2) Output (sinks: 1, sources: 0, priority: 100, available: yes)
        output:hdmi-surround71-extra1: Digital Surround 7.1 (HDMI 2) Output (sinks: 1, sources: 0, priority: 100, available: yes)
        ...
    Active Profile: output:hdmi-stereo
    ...

A certain profile can be set by command with format as this:

pactl set-card-profile output:hdmi-stereo <card name|number> <profile name>

According to the question for the four mentioned outputs the commands are:

pactl set-card-profile alsa_card.pci-0000_03_00.1 output:hdmi-stereo # LG ULTRAWIDE
pactl set-card-profile alsa_card.pci-0000_03_00.1 output:hdmi-stereo-extra1 # LG TV
pactl set-card-profile alsa_card.pci-0000_00_1b.0 output:iec958-stereo # Digital Output
pactl set-card-profile alsa_card.pci-0000_00_1b.0 output:analog-stereo # Headphones

As it is shown in this answer, when the new profile is set next things to do are:

 pacmd set-default-sink <sink number of the target profile>
 pacmd move-sink-input "$i" <sink number of the target profile> 
 # where $i is the index number of any active input: pacmd list-sink-inputs   

According to my needs, described in the question, I've created the following script:

#!/bin/bash

# Name: /usr/local/bin/audioswitch
# Usage: audioswitch; audioswitch 1; audioswitch 2;  audioswitch 3; audioswitch 4

CARD_1="pci-0000_03_00.1"             ### HDMI Audio Controller of NVidia GTX 660
CARD_1_PROFILE_1="hdmi-stereo"          # LG ULTRAWIDE
CARD_1_PROFILE_2="hdmi-stereo-extra1"   # LG TV
CARD_0="pci-0000_00_1b.0"             ### Built-in Audio
CARD_0_PROFILE_1="iec958-stereo"        # Digital Output
CARD_0_PROFILE_2="analog-stereo"        # Headphones

# Read the user's input
CHOICE="${@}"
choice() {
    if   [ "$CHOICE" == 1 ]; then CARD="$CARD_1"; PROF="$CARD_1_PROFILE_1" # LG ULTRAWIDE
    elif [ "$CHOICE" == 2 ]; then CARD="$CARD_1"; PROF="$CARD_1_PROFILE_2" # LG TV
    elif [ "$CHOICE" == 3 ]; then CARD="$CARD_0"; PROF="$CARD_0_PROFILE_1" # Digital Output
    elif [ "$CHOICE" == 4 ]; then CARD="$CARD_0"; PROF="$CARD_0_PROFILE_2" # Headphones
    else
        echo -e "\nYou should choice between:"
        echo -e "\n\t[1] LG ULTRAWIDE\n\t[2] LG TV\n\t[3] Digital Output\n\t[4] Headphones\n"
        echo -n "Your choice: "; read CHOICE; echo; choice; # call the function again
    fi
}; choice # call the function

# Set the choosen card profile as sink
pactl set-card-profile "alsa_card.${CARD}" "output:${PROF}";

# Set the default sink to the new one
pacmd set-default-sink "alsa_output.${CARD}.${PROF}" &> /dev/null

# Redirect the existing inputs to the new sink
for i in $(pacmd list-sink-inputs | grep index | awk '{print $2}'); do
    pacmd move-sink-input "$i" "alsa_output.${CARD}.${PROF}" &> /dev/null
done

The script is ready to be used with custom keyboard shortcuts, because it can handle the value (1-4) of the first positional parameter. When it is called without additional paraneter it will ask for your choice:

$ audioswitch 

You should choice between:

    [1] LG ULTRAWIDE
    [2] LG TV
    [3] Digital Output
    [4] Headphones

Your choice: 1