
die Lage
situation
The total set of circumstances or the current situation in which someone or something finds themselves.
Die politische Lage im Land ist derzeit sehr instabil.
The political situation in the country is currently very unstable.
situation / location
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situation
The total set of circumstances or the current situation in which someone or something finds themselves.
Die politische Lage im Land ist derzeit sehr instabil.
The political situation in the country is currently very unstable.

location
The geographical place or position of something, for example a building or a city.
Das Haus hat eine ruhige Lage am Stadtrand.
The house has a quiet location on the outskirts of town.

to be able
To have the ability or possibility to do something.
Nach seiner Knieoperation ist er wieder in der Lage, Sport zu treiben.
After his knee operation, he is able to do sports again.

position
The physical position or posture in which a person or object is located.
Der Arzt brachte den Bewusstlosen in die stabile Seitenlage.
The doctor put the unconscious person into the recovery position.

layer
A horizontal layer or level of material.
Für die Lasagne schichten wir eine Lage Nudeln und eine Lage Soße abwechselnd.
For the lasagna, we alternate a layer of noodles and a layer of sauce.
'Die Lage' (the situation/location/position) is closely related to the verb 'liegen' (to lie). It describes how or where something 'lies'—whether it is a situation, a place, or a position.
Das Hotel liegt sehr zentral. Die Lage ist also perfekt.
The hotel is very centrally located. So the location is perfect.
When 'Lage' (situation) means a situation, it is often combined with adjectives like 'politisch' (political), 'wirtschaftlich' (economic), 'schwierig' (difficult), or 'ernst' (serious). You can also say 'die Lage einschätzen' (to assess the situation) or 'die Lage ist angespannt' (the situation is tense).
Ein Experte soll die wirtschaftliche Lage des Unternehmens beurteilen.
An expert is supposed to assess the company's economic situation.
When 'Lage' (location) describes a place, typical adjectives are 'ruhig' (quiet), 'zentral' (central), 'sonnig' (sunny), or 'idyllisch' (idyllic). For example, people talk about the 'Lage eines Hauses' (location of a house).
Wir suchen eine Wohnung in ruhiger Lage.
We are looking for an apartment in a quiet location.
The phrase 'in der Lage sein, etwas zu tun' (to be able to do something) is a fixed expression and a more formal alternative to 'können' (can/be able to). It is always used with 'zu' and an infinitive at the end of the sentence.
Ich bin im Moment nicht in der Lage, Ihnen zu helfen.
At the moment, I am not able to help you.
In the meaning 'körperliche Position' (physical position), 'Lage' (position) is frequently used in medical contexts. The 'stabile Seitenlage' (recovery position) is a well-known first-aid measure.
Die Sanitäter brachten den Verletzten in eine sichere Lage.
The paramedics put the injured person in a safe position.
You can recognize this meaning from the context of materials that are placed on top of each other. Typical contexts are cooking (e.g., lasagna), geology (rock), or construction/painting (paint).
Der Maler trägt noch eine zweite Lage Farbe auf.
The painter applies a second layer of paint.
status / stand
Stand and Lage can both describe the current situation in negotiations. Stand focuses more on what has been achieved so far or how far something has progressed, while Lage covers all the circumstances that currently exist. Use Stand for progress so far and Lage for the overall situation.

Wegen der neuen Informationen ist die Lage bei den Verhandlungen unübersichtlich.
Because of the new information, the situation in the negotiations is unclear.
Der Stand der Verhandlungen ist heute besser als letzte Woche.
The status of the negotiations is better today than it was last week.