You could add a constraint to your first route so that it will only match numbers for the {id} parameter:
config.Routes.MapHttpRoute(
name: "ActionById",
routeTemplate: "api/Search/{action}/{id}",
defaults: new { controller = "Search", id = RouteParameter.Optional },
constraints: new { id = @"\d+" }
);
Alternatively you could remove your second route entirely and change your action signatures to use only the {id} parameter:
[HttpGet]
public IEnumerable<Object> CompanyByOrderId(long id) { ... }
[HttpGet]
public IEnumerable<Object> CompanyByName(string id) { ... }
[HttpGet]
public IEnumerable<Object> UserByName(string id) { ... }