übrig
left over
Describes something that is still present after something else has been used up or distributed; remaining.
Vom Kuchen ist nur noch ein kleines Stück übrig.
There is only a small piece of cake left over.

left over
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left over
Describes something that is still present after something else has been used up or distributed; remaining.
Vom Kuchen ist nur noch ein kleines Stück übrig.
There is only a small piece of cake left over.

The word 'übrig' (left over) is closely related to 'über' (over). It describes something that is 'over' what was needed or taken—so, the remainder.
Nach der Party sind viele Getränke übrig geblieben.
After the party, a lot of drinks were left over.
In the meaning 'verbleibend' (remaining), 'übrig' is almost always used together with the verbs 'sein' (to be) or 'bleiben' (to remain) at the end of the sentence. So it does not stand directly before the noun.
Ist noch Kaffee übrig?
Is there any coffee left?
The expression 'jemandem bleibt nichts anderes übrig, als ... zu ...' (someone has no choice but to ...) has a fixed structure. The person who has no choice is in the dative. The only option is expressed with an 'als ... zu + infinitive' construction.
Mir blieb nichts anderes übrig, als zu Fuß nach Hause zu gehen.
I had no choice but to walk home.
The expression 'etwas für jemanden/etwas übrig haben' (to care for someone/something; to have sympathy or appreciation for someone/something) always uses the preposition 'für' with the accusative. It is very often used in the negative form 'nichts für ... übrig haben' (to have no time/appreciation for ...; to reject ...), to express disapproval or rejection.
Für solche Ideen habe ich nichts übrig.
I have no appreciation for ideas like that.
available / present
'vorhanden' and 'übrig' can both say that something is there. The difference lies in how that comes about. 'Vorhanden' only means that something exists or is available. It sounds somewhat more factual or formal. 'Übrig' is used when something is left over after use, distribution, or selection. The words can be confused because in both cases something is there. In practical terms: 'vorhanden' asks about existence, while 'übrig' asks about what is left.

Nach dem Abendessen ist noch etwas Suppe übrig.
There is still some soup left over after dinner.
Für die Besprechung sind genug Stühle vorhanden.
There are enough chairs available for the meeting.