IEnumerable<object> a = new IEnumerable<object>(); Can I do this?

You can for example create an instance of List<object>, which implements IEnumerable<object>. Example:

List<object> list = new List<object>();
list.Add(1);
list.Add(4);
list.Add(5);

IEnumerable<object> en = list;
CallFunction(en);

Another solution would be to use Empty.

msdn extract:

Returns an empty IEnumerable that has the specified type argument.

IEnumerable<object> a = Enumerable.Empty<object>();

There is a thread on SO about it: Is it better to use Enumerable.Empty() as opposed to new List to initialize an IEnumerable?

If you use an empty array or empty list, those are objects and they are stored in memory. The Garbage Collector has to take care of them. If you are dealing with a high throughput application, it could be a noticeable impact.

Enumerable.Empty does not create an object per call thus putting less load on the GC.

Since you now specified you want to add to it, what you want isn't a simple IEnumerable<T> but at least an ICollection<T>. I recommend simply using a List<T> like this:

List<object> myList=new List<object>();
myList.Add(1);
myList.Add(2);
myList.Add(3);

You can use myList everywhere an IEnumerable<object> is expected, since List<object> implements IEnumerable<object>.

(old answer before clarification)

You can't create an instance of IEnumerable<T> since it's a normal interface(It's sometimes possible to specify a default implementation, but that's usually used only with COM).

So what you really want is instantiate a class that implements the interface IEnumerable<T>. The behavior varies depending on which class you choose.

For an empty sequence use:

IEnumerable<object> e0=Enumerable.Empty<object>();

For an non empty enumerable you can use some collection that implements IEnumerable<T>. Common choices are the array T[], List<T> or if you want immutability ReadOnlyCollection<T>.

IEnumerable<object> e1=new object[]{1,2,3};
IEnumerable<object> e2=new List<object>(){1,2,3};
IEnumerable<object> e3=new ReadOnlyCollection(new object[]{1,2,3});

Another common way to implement IEnumerable<T> is the iterator feature introduced in C# 3:

IEnumerable<object> MyIterator()
{
  yield return 1;
  yield return 2;
  yield return 3;
}

IEnumerable<object> e4=MyIterator();