Bismillah. These also apply to orphans who are fostered or adopted, of course. This is written in the hope that it will be of benefit to individuals, charities and other agencies that help orphans.
One of the inspirations to do this was recently meeting an elderly Somali-Yemeni woman in London who is fostering two Afghani orphans with the help of the UK welfare state.
ISLAMIC TEACHINGS ABOUT ORPHANS
Did He not find you orphaned, and give you shelter? … So as for the orphan, do not oppress! (Qur’an 93: 6 & 9)
Piety is not to face east or west in prayer, but piety is to have faith in God … and to spend of your wealth, out of love for God and despite your love of wealth, on relatives, orphans, the needy and others … (Qur’an 2:177)
The righteous, they give food, out of love for God and despite their love of food, to the needy, the orphan and the prisoner. (Qur’an 76:8)
The following are sound (sahih) traditions, except where indicated, recorded in Imam Bukhari’s al-Adab al-Mufrad, nos. 131-140, in chapters about orphans.
“One who strives on behalf of the widow and the needy is like the one who fights in the path of God, or fasts by day and stands in prayer by night.” – The Prophet, peace be upon him. 
“Whoever is tested with young daughters [including orphans] and shows kindness to them: they will be a barrier between him or her and the Fire.” – The Prophet, peace be upon him. 
“I and the one who takes care of an orphan will be like these two in the Garden.” – The Prophet, peace be upon him, indicating with his forefinger and middle finger. 
Abdullah, son of Omar, Companion of the Prophet (peace be upon him), would not eat without one or more orphans sharing his meal.
An orphan used to eat at mealtimes with Abdullah, son of Omar, Companion of the Prophet (peace be upon him). Once, he arrived late and the food had all been eaten, so Abdullah brought him some porridge with honey. 
“The best of homes are those where an orphan is shown kindness. The worst of homes are those where an orphan is shown cruelty.” – attributed to The Prophet, peace be upon him. 
“Be to an orphan like a merciful father or mother.” – Dawud 
A man asked Ibn Sirin , “How should I treat an orphan under my care?” He replied, “Exactly as you treat your own child.”
 Also in Sahih al-Bukhari & Sahih Muslim.
 Also in Sahih al-Bukhari.
 Narration weak; meaning sound.
 Narration weak; meaning sound. Also in Sunan Ibn Majah.
 A disciple of the Companions of the Prophet (peace be upon him).