Does query task api supports orderby and OR operator clause

See:

Yes, for example:

  public getTasks(): Observable<any> {

    const endpoint = `${this.processEngineUriPrefix}runtime/tasks`;

    const sort = 'createTime';
    const order = 'desc';

    const params = new HttpParams().set('sort', sort).set('order', order);

    return this.httpClient.get<TaskListModel>(endpoint, this.getHttpOptions(params))
      .pipe(
        tap(() => {
          this.logger.info('TasksService: getTasks() completed');
        }),
        catchError(this.handleError('getTasks', []))
      );

  }

Also see: Upcomig task for a user