According to Hindu literature, how Asuras (demons) are interacting with Maya? What are relevant passages where someone can start studying about this?
The chapter 16 of Srimad-Bhagavad-Gita deals with the characteristics ot the Asuras (demons).. One sloka from the chapter states
16.18 Resorting to egotism, power, arrogance, passion and anger, hating Me in their own and others' bodies, (the demons become). envious by nature.
In other slokas also, Sri Krishna states that the Asuras are guided by desires (kama) and anger (krodha).
In chapter 3, Sri Krishna says that desire and anger originate from the Rajo-guna:
3.37 The Blessed Lord said This desire, this anger, born of the quality of rajas, is a great devourer, a great sinner. Know this to be the enemy here.
Rajoguna is one of the three gunas, and all the three are the basic elements of Maya :
7.13 All this world, deluded as it is by these three things made of the gunas (qualities), does not know Me who am transcendental to these and undecaying.
7.14 Since this divine Maya of Mine which is constituted by the three gunas is difficult to cross over, (therefore) those who take refuge in Me alone cross over this Maya.
Sri Ramakrishna in His Kathamrita terms these bad qualities as 'Avidya-Maya' by the way as opposed to Vidya-Maya that give birth to jnana, bhakti, viveka, vairagya etc.
God incarnates repeatedly to kills the demons as described in the different Puranas.The Mother Goddess known as Mahamaya announces in Sri Sri Chandi (chapter 11, mantra 55):
ittham yada yada vadhaa danabotthaa vabishyati/tadaa tadaa abatirya aham karishyaami ari-sankshayam//
meaning : Whenever such obstacles caused by the demons will be created, I will appear and destroy these enemies.