What US Visa do I need to perform in a theatre

You would most likely need one of the following visas. Each of them has different additional criteria:

• O-1B: this requires "sustained national or international acclaim." In particular, it requires "distinction," which is defined thus:

Distinction means a high level of achievement in the field of the arts evidenced by a degree of skill and recognition substantially above that ordinarily encountered to the extent that a person described as prominent is renowned, leading, or well-known in the field of arts.

• P-2: this requires participation in "a reciprocal exchange program between an organization in the United States and an organization in another country." For example, I've seen several plays on Broadway that note that the British actors performing, who are not members of the Actors' Equity Association, are performing under a reciprocal arrangement (with, I suppose, British Equity, though I do not remember for certain).

• P-3: this requires cultural "uniqueness," so whether you qualify will depend somewhat on the nature of the performance which you've been offered.

The host or organizer of your performance would need to file an application with USCIS for an O-1B visa on your behalf, and you would need to show that you have "extraordinary ability in the arts" through things like press reviews, awards, grants, etc.

The USCIS page describing O-1 visas is here.

The 'petitioner' (your host) first needs to file an I-129 "Petition for Nonimmigrant Worker", and this should be filed at least 45 days beforehand.
In addition to evidence of your ability, your host must show a copy of a written contract or a summary of an oral contract between you and them and an itinerary describing your planned performances.
Evidence of your ability is described as:

Evidence that the beneficiary has received, or been nominated for, significant national or international awards or prizes in the particular field, such as an Academy Award, Emmy, Grammy or Director's Guild Award, or evidence of at least (3) three of the following:

• Performed and will perform services as a lead or starring participant in productions or events which have a distinguished reputation as evidenced by critical reviews, advertisements, publicity releases, publications, contracts or endorsements
• Achieved national or international recognition for achievements, as shown by critical reviews or other published materials by or about the beneficiary in major newspapers, trade journals, magazines, or other publications
• Performed and will perform in a lead, starring, or critical role for organizations and establishments that have a distinguished reputation as evidenced by articles in newspapers, trade journals, publications, or testimonials.
• A record of major commercial or critically acclaimed successes, as shown by such indicators as title, rating or standing in the field, box office receipts, motion picture or television ratings and other occupational achievements reported in trade journals, major newspapers or other publications
• Received significant recognition for achievements from organizations, critics, government agencies or other recognized experts in the field in which the beneficiary is engaged, with the testimonials clearly indicating the author's authority, expertise and knowledge of the beneficiary's achievements
• A high salary or other substantial remuneration for services in relation to others in the field, as shown by contracts or other reliable evidence

If the above standards do not readily apply to the beneficiary’s occupation in the arts, the petitioner may submit comparable evidence in order to establish eligibility (this exception does not apply to the motion picture or television industry).

As you are working, you need a temporary work visa.

This link tells you the different work visa categories, depending on your education.

This link lets you apply depending on your country.

You cannot work on a visit/business visa.