stopfen
to stuff
To press or force something with pressure into a narrow opening or a limited space.
Er stopfte seine schmutzige Wäsche einfach in den Rucksack.
He simply stuffed his dirty laundry into the backpack.

to stuff / darn
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to stuff
To press or force something with pressure into a narrow opening or a limited space.
Er stopfte seine schmutzige Wäsche einfach in den Rucksack.
He simply stuffed his dirty laundry into the backpack.

'Stopfen' does not mean 'stoppen' (to stop) or 'anhalten' (to halt). It does look similar to the English 'to stop', but its actual meaning is 'etwas mit Druck irgendwo hineinpressen' (to stuff, to cram something somewhere with pressure).
Ich muss noch alle meine Kleider in den kleinen Koffer stopfen.
I still have to stuff all my clothes into the small suitcase.
The verb 'stopfen' (to stuff) is related to the noun 'der Stopfen' (cork, plug). Both words share the basic idea of filling or closing an opening.
Er benutzte einen alten Lappen, um das Loch in der Wand zu stopfen.
He used an old rag to plug the hole in the wall.
When you want to express that something is being pressed into a tight space, use the preposition 'in' followed by the accusative.
Sie stopfte schnell das letzte T-Shirt in die bereits volle Tasche.
She quickly stuffed the last T-shirt into the already full bag.
In the meaning 'ein Loch flicken' (to mend a hole), 'stopfen' (to darn) is used almost exclusively for textiles. The most common combination is 'Socken stopfen' (to darn socks).
Meine Großmutter hat mir gezeigt, wie man Löcher in Socken stopft.
My grandmother showed me how to darn holes in socks.
The colloquial meaning 'gierig essen' (to eat greedily) is used reflexively: 'sich stopfen' (to stuff oneself). It is often supplemented with the preposition 'mit' plus the dative to say what is being eaten.
Die Kinder haben sich auf der Party mit Süßigkeiten gestopft.
The children stuffed themselves with sweets at the party.
When 'stopfen' (to constipate) describes an effect that inhibits digestion, the subject of the sentence is a food item and the verb is used without an object. It describes a property of the food.
Man sagt, dass zu viel Kakao bei kleinen Kindern stopft.
People say that too much cocoa is constipating for small children.
to stick / to be stuck
'stecken' and 'stopfen' both have to do with putting something into a tight space. 'stecken' sounds more neutral and often means that something goes into an opening and stays there. 'stopfen' emphasizes pressure: it is tight, full, or something does not really fit well inside. That is why you would more likely say 'den Stecker in die Steckdose stecken' (to plug the plug into the socket), but 'Kleidung in einen vollen Koffer stopfen' (to stuff clothes into a full suitcase). 'stopfen' often feels a bit rougher or more hurried than 'stecken'.

Vor der Reise stopft Max noch zwei Pullover in den vollen Rucksack.
Before the trip, Max stuffs two more sweaters into the full backpack.
Der Mitarbeiter steckt die Karte in das Lesegerät.
The employee inserts the card into the reader.