Here's a chart from OS X Keyboard Shortcuts that lists all the main icons, their primary names, and alternate names/symbols:

This Apple fansite has a similar list on a page with other Mac hints.
OS X Keyboard Shortcuts also provides descriptions for the most commonly seen icons. This official Apple site is similar, but is targeted at new users making the switch from Windows.
And as a bit of historical trivia, this Folklore.org blog post explains where the Command icon came from. The original idea was to use the Apple logo, but Steve Jobs decided there were "too many Apples on the screen!" and ordered a change. The icon you call "weird" and "like a clover" actually started life as the campground symbol on Swedish road signs.
I remember seeing some of these icons drawn on the keyboards of older Apple computers; why they were discontinued, I don't know.
(An earlier revision of this answer contained links to Apple documentation that stopped working.)
Answer from Pops on Stack Exchangemacos - Full list of option key mappings in Mac US keyboard - Ask Different
How to type Mac-specific symbols like ⌘ and ⌥ and ⇧
Some extremely useful Mac keyboard shortcuts that I use daily. Tell me yours.
Can we make a list of common keyboard symbols for Mac?
Videos
Here's a chart from OS X Keyboard Shortcuts that lists all the main icons, their primary names, and alternate names/symbols:

This Apple fansite has a similar list on a page with other Mac hints.
OS X Keyboard Shortcuts also provides descriptions for the most commonly seen icons. This official Apple site is similar, but is targeted at new users making the switch from Windows.
And as a bit of historical trivia, this Folklore.org blog post explains where the Command icon came from. The original idea was to use the Apple logo, but Steve Jobs decided there were "too many Apples on the screen!" and ordered a change. The icon you call "weird" and "like a clover" actually started life as the campground symbol on Swedish road signs.
I remember seeing some of these icons drawn on the keyboards of older Apple computers; why they were discontinued, I don't know.
(An earlier revision of this answer contained links to Apple documentation that stopped working.)
You can activate the "Character palette":
- Go to System preferences
- Select International
- Click on the Input menu tab
- At the bottom, check the box Display the input menu in the menu bar
- At the top, check the box Character palette


PS: My system being in French, I am translating these options back to English...
You can easily see how all the keys are mapped with Apple's Keyboard Viewer.
Here is a great resource that has the keyboard layout for Option key mappings (https://keyshorts.com/blogs/blog/41999105-the-ultimate-guide-to-macbook-keyboard):
If you want to type special characters or accents, press Option and the corresponding key according to the map below:

Use the Text Replacements tool like the one that’s built-in to macOS, iPadOS, and iOS, or a similar third-party tool like typeit4me or textexpander.
Choose the special character you want to add, and then choose a shortcut that, when typed, will be replaced with that special character.
Add the shortcut, then copy & paste the special character from this message.
You can use a shortcut like cmd or commandkey for ⌘.
I prefer to just precede the name of the special key with a semicolon, so my shortcut is ;command.
The special symbols are shown below, along with their official names, and my shortcuts.
⌘ Command ;command
⌥ Option ;option
⇧ Shift ;shift
⌃ Control control
↵ Return ;return
⌫ Backspace ;backspace
⌦ Delete ;delete
⏏ Eject ;eject
Apple logo ;apple Note: This last one only works on Apple devices.
UPDATE: I have made updated post with more shortcuts. Check it out here.
https://www.reddit.com/r/mac/comments/1hpk0rq/40_essential_mac_keyboard_shortcuts_to_boost/
Shortcuts
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Command+H - Hides the front window
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Option+Command+H - Hides all other windows except the front window
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Command+Tab - Switch between apps
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Command+L in safari to switch to url bar
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Command+1/2/3/4 to switch view in finder
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Space to quick view selected file
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Right click on closed settings app to quickly jump to any settings
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Command+Option+v to move the copied file
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Command+Q - Terminate the front window app
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Command+W - Close the front window. To close all windows of that app add Option key.
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Command+M - Minimize the front window. To minimize all windows of that app add Option key.
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Command+Option+Space open finder search
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Control+Command+F - Full screen/exit
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Command+` - Switch between an app opened windows
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Command+, - Open app settings page
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Command+G - Next search
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Command+Shift+C - Open computer window in finder
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Command+R - Opens original location of selected alias or shortcut in finder
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Enter button after selecting file to rename
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Command+E - Eject the selected .dmg or a removable media
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Shift+Command+. - Show hidden files in finder
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Command+Shift+brackets - Previous and next tab in safari
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Option+Command+esc - Open task manager
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Fn+Q - Make a new note in a new window
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Option+Right arrow on a folder in list view in finder to expand all folder, alternatively Option click the disclosure arrow icon. Option+Left arrow to reverse. Right and left arrow to expand the selected folder only.
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Command+Control+D - Alternative for Force Touch. I bind it to my mouse middle button click
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Command+Option+I - “Get Info” of multiple selected items together in finder
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Command+tab - Switch to last used app
What shortcuts do you use daily?
Your qwertyuiop result indicates that your machine thinks that both option and shift are being held down while you type. The symbols are not random but exactly what is supposed to happen when those keys are depressed. Normally this would indicate a damaged keyboard, especially if you try another one and it works ok.
I just ran into this issue myself. Was able to get out of it by hitting [option] [caps lock].