It is not usual to feel parasites moving inside your stomach, with the possible exception of a massive infestation where your gut is overloaded with parasites. However, this type of situation is quite rare, especially in developed countries where parasitic diseases are treated. As such, the scientific literature does not mention parasitic movements susceptible to be felt by the infected person.
In fact, it is quite usual to feel movements in the stomach. Many things, such as air bubbles or faeces that move within the gut, could cause it. The normal periodic peristaltic movements of the gastrointestinal system required to digest food could also cause it. However, this feeling could be interpreted as anything, meaning that a person anxious about actually or potentially having an intestinal parasite can interpret these movements as parasite(s) moving inside its stomach. It is the same thing that happens when a woman that had been recently pregnant feels something moving in her stomach and immediately thinks about a baby moving inside her.
It is more common, although not frequent, to feel and see parasite(s) or larvae moving under the skin. This manifestation is usually accompanied with other related symptoms, such as pain, itching and skin rashes. For instance, it is common to see the filarial nematode Loa loa crawling under the skin. Other parasites, such as the nematode Dracunculus medinensis responsible for the guinea worm disease, will eventually come out of the skin in order to fulfill its life cycle. This occurs mainly from the lower leg and generates a lot of burning pain. When it happens, it is possible to actually see the worm emerging from the skin.
Even though it is actually possible but rare to feel parasites moving under the skin, a form of psychosis called delusional parasitosis might be involved in some cases. In fact, people suffering from delusional parasitosis are persuaded that they feel parasites crawling under their skin, even though they are not affected by any parasites. These people are then susceptible to harm themselves by trying to kill or the remove the fictional parasite. On the other hand, these people can also be persuaded that they are harbouring ectoparasites, such as fleas and lice, on their skin or in their hair. Even though the classical clinical presentation of delusional parasitosis involve usually the false sensation of parasites crawling under the skin, the definition of this disease could potentially be extended to the people persuaded that they are infected by intestinal parasites and that they feel them move inside their body. It is important to note that delusional parasitosis is often associated with hypochondriasis, which is an excessive form of worry about the health experienced by people persuaded to have many types of diseases, other mental illnesses or drug abuse.
Finally, if you are experiencing movements in your stomach, it is probably just gas or something else rather than parasites. It is best not to worry too much about it. Furthermore, as Internet is a good source of disinformation about subject like this one, it is best to avoid reading discussion forum messages about this. In fact, worrying about it could be more dangerous for your health than the actual movements that you feel inside you.
Sources: Centers for Disease Control and Prevention, Merck Manual