Nala and Nila were valiant Vanaras and fought against Ravana. They were born due to boons from the Devatas. The names seems similars but they are not twins not even brothers. The twins in the Vanara army were Mainda and Dvivida.
###Nala
He was the son of divine Architect Vishwakarma. He acquired skills just like his father.
धनदस्य सुतः श्रीमान् वानरो गन्धमादनः |
विश्वकर्मा तु अजनयन् नलम् नाम महा कपिम् || १-१७-१२
The brilliant Gandhamaadana is the son of Kubera, while the divine architect Vishvakarma procreated the great monkey called Nala. [1-17-12]
Nala was the one who built Rama Setu. The ocean God advised Sri Rama to build a bridge over the ocean to Rama and recommends the name of Nala because he was the son of Vishwakarma. He was equal to his father in skill. Vishwakarma bestowed a boon to Nala and he would be equal to him in prowess.
The ocean God says this to Rama before the bridge was constructed.
"O, excellent man! This one, named Nala, a glorious person, is the son of Vishvakarma; who was given a boon by his father and is equal to Visvakarma." [5-22-44]
Let this greatly energetic monkey build a bridge across me. I can hold that bridge. He is just the same as his father. [5-22-45]
Hearing this from Sagara, Nala who was silent stood and spoke up as follows.
The great Ocean disclosed a truth. I will construct a bridge across this large Ocean, taking recourse to the skill and ability of my father. "On the mountain of Mandara, the following boon was given by Visvakarma to my mother: O, god like lady! A son equal to me will be born to you. I am a son born of Visvakarma's own loins. I am equal to Visvakarma. This god of Ocean has reminded me. The great ocean spoke the truth. Being unasked, I have not told you my details earlier. I am capable of constructing a bridge across the ocean. Hence, let the foremost of monkeys build the bridge now itself. [5-45-47]
Hearing the words of mighty Vanara Nala, Rama and thousands of vanaras rejoiced in joy and started the construction of the bridge.
Nala was able to construct a long bridge due to the boon of Vishwakarma. Ocean God promised that he would be able to hold the bridge built by him. So, the rocks, trees and boulders brought trees for constructing the bridge.
###Nila
Nila was also a valiant Vanara equal to Sugriva in might, courage and prowess. He was the son of Agni. He was one of the commanders of the Vanara army.
पावकस्य सुतः श्रीमान् नीलः अग्नि सदृश प्रभः |
तेजसा यशसा वीर्यात् अत्यरिच्यत वीर्यवान् || १-१७-१३
The bright son of Fire is Neela whose blaze is like that of fire and who excels other monkeys by his in resplendence, renown and courage. [1-17-13]
Nila was not the one who designed the plan for Ram setu bridge but he was one of very few Vanaras who could cross the ocean by flight. Hanuman thinks as follows:
चतुर्णामेव हि गतिर्वानराणां महात्मनाम् |
वालिपुत्रस्य नीलस्य मम राज्ञश्च धीमतः || ५-२-३०
Only four great Vanaras can come here - the son of Vali (Angada), Nila, myself and the wise king Sugriva. [4.2.30]
Even Ravana knew the courage and valour of Nila. When Hanuman was destroying Ashoka vana and killing the rakshasas sent by Ravana, he thinks and says this to his ministers.
दृष्टा हि हरयः शीघ्रा मया विपुल विक्रमाः |
वाली च सह सुग्रीवो जाम्बवान् च महाबलः || ५-४६-१०
नीलः सेना पतिः चैव ये च अन्ये द्विविद आदयः |
न एव तेषाम् गतिः भीमा न तेजो न पराक्रमः || ५-४६-११
Earlier, I saw the monkeys of a great prowess like Vali and Sugreeva, the mighty Jambavan, Nila the Chief of army and so on like Dvivida. their scheme of performance is not so fearful as this; nor their efficacy, nor their prowess, nor their intellect, nor this capacity to change their form or energy at will. [4.46.10]
Both the Vanaras were part of Vanara army led by Sugriva. So, these met Sri Rama after meeting Sugriva.