The task I've been given is to "use the gerund form after these verbs":

I enjoy going to parties where I don't know anyone.

I avoid expressing my feelings and ideas in public.

I don't mind giving up my time to help other people.

Secondly, I need to "use the gerund or infinitive form after these verbs":

I can't stand being /to be in a messy room.

Lastly, I need to "use the gerund form after these expressions containing prepositions":

I insist on making my own decisions.

Are the examples you cite intended to be your answers to the task?

"Going to parties", "expressing my feelings" and "giving up my time" are indeed gerund-participial clauses.

Thank you for your response...I copied the task page exactly how it has been sent to me. I am teaching conversational English to ESL students and I need to go through these tasks with them. How would you explain a 'gerund-participial clause' to someone where English is their second language? This feels quite complicated. I need to keep it as simple as possible.

Students: We have free audio pronunciation exercises.

Modern grammar does not distinguish gerunds and present participles, but simply calls all -ing forms 'gerund-participles'. It's a better and simpler way of handling such forms.

Gerund-participle verb-forms function as heads of the non-finite clauses in which they occur. These clauses are called 'gerund-participial' clauses.