In certain Pagan traditions in the West especially Goetia, demons are summoned by rituals mainly for material purposes. Can Asuras and Rakshasas be summoned in Hinduism by rituals? If yes, for what purposes?
Not sure if there are many but found couple of instances that sort of invoke Asura/Asuri:
The Book 1 of Ṛgveda describes Savitr as an Asura who is a "kind leader" and help is asked from him against Rākṣasas and Yatudhanas.
हिरण्यहस्तो असुरः सुनीथः सुमृळीकः स्ववाँ यात्वर्वाङ् । अपसेधन्रक्षसो यातुधानानस्थाद्देवः प्रतिदोषं गृणानः ॥१०॥
Meaning: May he, gold-handed Asura, kind leader, come hither to us with his help and favor. Driving off Rākṣasas and Yatudhanas, [he] the god is present, praised in hymns at evening.
May the golden-handed, life-bestowing, well-guiding, exhilarating and affluent Savitri [Asura] be present; for the deity, if worshipped in the evening, is at hand, driving away Raksasas and Yatudhanas.
In Book 7, Asuri is a powerful female with the special knowledge of herbs, who uses that knowledge to seduce Deva Indra in Atharva Veda. A hymn invokes this special power in Asuri, and this hymn is stipulated for a woman as a charm to win over the lover she wants.
I dig this Healing Herb that makes my lover look on me and weep, That bids the parting friend return and kindly greets him as he comes. This Herb wherewith the Asuri drew Indra downward from the Gods, With this same Herb I draw thee close that I may be most dear to thee. Thou art the peer of Soma, yea, thou art the equal of the Sun, The peer of all the Gods art thou: therefore we call thee hitherward. I am the speaker here, not thou: speak thou where the assembly meets. Thou shalt be mine and only mine, and never mention other dames. If thou art far away beyond the rivers, far away from men, This Herb shall seem to bind thee fast and bring thee back my prisoner. — A maiden's love-charm, Atharva Veda, Hymn 7.38,
The powers of an Asuri are projected into plants offering a remedy against leprosy.
First, before all, the strong-winged Bird was born, thou wast the gall thereof. Conquered in fight, the Asuri took then the shape and form of plants. The Asuri made, first of all, this medicine for leprosy, this banisher of leprosy. She banished leprosy, and gave one general colour to the skin. — A charm against leprosy, Atharva Veda, Hymn 1.24,