schwingen
to swing
To move back and forth evenly and rhythmically around a central point or resting position.
Das Pendel der alten Uhr schwingt langsam hin und her.
The pendulum of the old clock swings slowly back and forth.

to swing
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to swing
To move back and forth evenly and rhythmically around a central point or resting position.
Das Pendel der alten Uhr schwingt langsam hin und her.
The pendulum of the old clock swings slowly back and forth.

The verb 'schwingen' (to swing) is closely related to the noun 'der Schwung' (momentum/swing). All meanings of the verb have to do with a sweeping, arcing, or rhythmic movement.
Mit viel Schwung sprang sie über den Graben.
With a lot of momentum, she jumped over the ditch.
Grammar helps distinguish the meanings. 'Sich schwingen' (to swing oneself) is reflexive and means to move onto something. 'Etwas schwingen' (to swing something) is transitive and means to move something. If the subject alone 'schwingt' (swings/oscillates), it oscillates.
Der Affe schwang sich von Ast zu Ast.
The monkey swung itself from branch to branch.
In the meaning 'to move onto something', the verb is always reflexive ('sich schwingen'). It is almost always followed by a preposition that indicates direction, e.g. 'auf' (onto), 'in' (into), 'über' (over), or 'von' (from).
Der Dieb schwang sich über den Zaun und rannte davon.
The thief swung himself over the fence and ran away.
When 'schwingen' (to swing) is used transitively, meaning it has an accusative object, typical objects are things you hold in your hand or move with your body: die Hüften (the hips), eine Keule (a club), einen Tennisschläger (a tennis racket), einen Taktstock (a baton).
Die Tänzerin schwang ihre Hüften im Rhythmus der Musik.
The dancer swung her hips to the rhythm of the music.
The expression '(große) Reden schwingen' (to make grand speeches) is a fixed combination and means to give a long, often somewhat pompous speech. It is frequently used with a slightly ironic or critical undertone.
Der Politiker ist gut darin, große Reden zu schwingen, aber es passiert wenig.
The politician is good at making grand speeches, but little actually happens.
In this meaning, 'schwingen' (to oscillate) is used in a scientific or musical context. It describes the physical movement of waves, strings, or other systems capable of oscillation.
Die Saite der Geige schwingt und erzeugt so den Ton.
The violin string oscillates and thus produces the tone.
to hold
'eine Rede halten' (to give a speech) and 'eine Rede schwingen' (to make a speech) both mean that someone speaks in front of others. 'eine Rede halten' is the normal and neutral expression. It fits celebrations, meetings, exams, or official occasions. 'eine Rede schwingen' often sounds slightly mocking or exaggerated. It is used when the speech seems long, loud, very solemn, or a bit too self-important. The words can be confused because both are connected with a speech. If you want to stay neutral, 'eine Rede halten' is almost always safer.

Beim Abendessen schwang Paul wieder eine lange Rede über gesunde Ernährung.
At dinner, Paul once again launched into a long speech about healthy eating.
Die Direktorin hält bei der Abschlussfeier eine kurze Rede.
The principal gives a short speech at the graduation ceremony.