I would go to his paediatrician and tell them the things that concern you and ask for a multi disciplinary team assessment by professionals who have experience of diagnosing autistic spectrum disorders.
He is at that age when other children are becoming more social and he isn't. That is why you are starting to notice the social differences eg. playing parallel, on the outside of the groups during playtime etc. He will develop in this area, but he will need adult support to help him initiate and sustain play and he will need to be taught some very basic social skills that we take for granted - such as holding a two way conversation.
Lack of eye contact is common. Some individuals say that making eye contact makes them very uncomfortable. I wouldn't force eye contact, and neither would a school that had experience of autistic spectrum disorders. It can also sometimes be down to sensory processing difficulties. For example, my son cannot look at anyone whilst he is talking. If he looks into their eyes he cannot gather his thoughts to speak, or if they are speaking to him he cannot remember what they said. So there can be difficulties with 'multi-tasking' from a sensory point of view. Your son may drift around the classroom for the same reason. He cannot listen and look at the teacher at the same time. He needs his speech testing by a Speech and Language Therapist. They should assess his receptive as well as his expressive speech along with auditory memory, working memory, auditory processing etc. The SALT is also the professional who assesses social interaction skills and they should put together a programme of supports eg. social skills club, mentoring or circle of friends, dinnertime clubs etc.
He is only 3 now, but by the time all the assessments are done and recommendations are being put into place, he will probably be nearly 4. And without these supports, therapies and structure he will struggle which will affect his self esteem.
My now 12 year old son was diagnosed with Asperger's approximately a year and a half ago. I had never heard of such a thing until his teacher talked to me and shared her suspicions that he may have it. I was very sceptical at first as well as slightly offended. I decided to research it however. I was astonished to see a list of signs/symptoms of Asperger's....they described my son completely. I then took him to see a psychiatrist who confirmed the diagnosis. He was also diagnosed with ADD.
My son is INCREDIBLY SMART and very adult-like. He always has been. The things that you have described sounds a great deal like my son. I would encourage you to research Asperger's as much as possible. There is a wealth of information online, as well as many books that are available at large bookstores.
My son has also learned a lot about Asperger's. He's actually quite proud that he has it! There are a lot of famous and well-respected individuals that share his same syndrome. It actually has a lot of benefits :-)
Many of the difficulties that you describe sound typical of 4 year old children. For example, difficulty transitioning from play to clean up is very common. Nevertheless, I recommend that you discuss your concerns with your pediatrician. Early intervention is vitally important, and I recommend that parents share all developmental concerns with their pediatrician or other qualified professional who can assess the child's development in person and in detail.