strömend
pouring
Describes a liquid, especially rain, that flows in large quantities and without interruption.
Bei strömendem Regen warteten wir auf den Bus.
We waited for the bus in the pouring rain.

pouring / streaming
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pouring
Describes a liquid, especially rain, that flows in large quantities and without interruption.
Bei strömendem Regen warteten wir auf den Bus.
We waited for the bus in the pouring rain.

The word 'strömend' (pouring/streaming) is the present participle of the verb 'strömen' (to flow, to move in one direction). Like other participles, it can be used as an adjective to describe an ongoing action.
Die strömende Menge bewegte sich langsam in Richtung Ausgang.
The streaming crowd moved slowly toward the exit.
'Strömend' (pouring/streaming) is used almost exclusively as an adjective directly before a noun (attributively). Using it as a stand-alone predicate, e.g. 'Der Regen ist strömend' (the rain is pouring), is uncommon and sounds unnatural.
Trotz des strömenden Regens machten wir einen Spaziergang.
Despite the pouring rain, we went for a walk.
By far the most common and fixed collocation for this meaning is 'strömender Regen' (pouring rain). This combination is often used as a unit to describe heavy, continuous rain.
Wir konnten wegen des strömenden Regens nicht nach draußen gehen.
We couldn't go outside because of the pouring rain.
ongoing / continual
'laufend' and 'strömend' can both describe a flowing movement. 'laufend' mainly fits water that is flowing, for example from a tap or in a stream. 'strömend' feels stronger: it describes liquid flowing in large quantities and without stopping, especially rain. In a figurative sense, 'strömend' can also be used for light or many people. 'laufend' is more neutral here, while 'strömend' emphasizes the amount and force of the movement.

Nach dem Konzert kamen die Menschen strömend aus der Halle.
After the concert, people streamed out of the hall.
Unter dem laufenden Wasser wusch sie schnell die Äpfel ab.
She quickly rinsed the apples under the running water.