Where are you looking to move to? That part really sets up your strategy. Huge difference between looking for jobs in NYC versus Miami, for instance. 

Don't worry about using samples of work in your portfolio. You are not using any of it for commercial purposes. Don't show entire construction document sheets though. Isolate individual details and such. Best is to show photos of completed work. 3 years in you should hopefully have some. 

Don't worry about references. Your contributions to projects should speak for themselves. Make it clear what your exact contributions were. 

Revit knowledge is absolutely critical. How have you worked in architecture for 3 years without any exposure to it? You can still pick up basics of that software pretty quickly if your understanding of project documentation is solid. Otherwise this is your biggest handicap right now. 

You are at a career point where anything is still possible, so good on you for being proactive. You will have to go to in person interviews, so make sure your budget allows for impromptu trips.

In NYC, a lot of firms are starting to use Skype to interview. That said, you will have WAY more success if you just show up to whichever market you want to work in. I have moved multiple times. Firms want to know they are hiring someone who will actually show up on the first day... not someone who wants to move and may still be in that process when they need someone at the helm. 

Also... my biggest advice for someone leaving their first gig after being there a few years: grab all you can on the way out. Make sure you have all the high-res images and PDFs of all relevant drawings of the projects you have worked on. I only grabbed a few drawings of 2 projects after I left my first job. Years later, I wish I had all the details and MEP sets. It helps to reference projects you know well later in life when tryign to figure out little things. 

Also... use Lynda.com to learn Revit if you need to teach yourself. This can be free if you have a local library card or an .edu email. 

Also, do firms typically contact your current firm if they are considering you? It would suck to have a potential firm contact your current firm, they either don’t hire you or after interviewing you decide it’s not a good fit after all, and then now your current firm has been tipped off opening the door for potential consequences.

Firms will not typically contact your current employer.  Just to be sure, tell the firms to which you're applying that you're currently employed but "discreetly investigating new opportunities".

Generally once I was sure I was leaving a firm and had already given notice, then I would ask - by email, so I had a written record - if I could take some samples of my work for my portfolio.  I never had anybody say no, and actually if the firm is an AIA member firm, the AIA's code of conduct says that employers agree to allow employees to take work samples (at the employee's expense for any printing or copying or whatever, and within a reasonable period of leaving - i.e. you can't expect to come back years later and request them.)  Taking work samples for your portfolio without asking is tricky: I think most people do that when they are interviewing while still employed - but the work is the property of the employer, so technically it's not ok. If you're doing that I'd suggest at least blacking out or removing any identifying info about the project location and owner, so as not to violate any contractual agreements that your current firm might have with clients re privacy or dissemination of the drawings.

References: it's not typical to list references on the resume anymore - it's implied that you'll be able to provide contact info for references if asked. Some people include reference letters in their portfolio - this is more common if the employer was in another country, or for some other reason would be difficult or impossible to contact directly (retired, relocated to parts unknown, deceased...)  It's not a bad idea to ask for letters of reference when you leave a firm, if you're on good terms with some people there who would be appropriate references - but you'll find that most firms will want to call your references directly anyway. I agree with you that using anybody at your current firm as a reference while you're still employed there is a bad idea unless you're ok with the whole firm knowing you're looking elsewhere.  Good people to use as references would be previous employers - whether or not they were in architecture; former coworkers or classmates who are employed at other architecture firms; other professional contacts.

It is very rare for a firm, especially in NYC, to seriously consider a remote candidate with whom they have no familiarity. Quite a few firms will post in their ad 'local candidates only' etc. this is even more true for lower level positions, for which there are ample candidates / recent grads from the neighboring schools. There has been a surge of job ads in the past six months so you may have a slightly better shot but I wouldn't count on it. Not sure what msp is talking about to be honest, that is some rather false hope.

Unclear if OP is interested in NYC, but generally for a move to a large metro, with no friends/network on the other side, and minimal work experience, you're going to need a local address and be ready for in person interviews with only a few days notice. Aka a fat savings and plan to be unemployed and searching for a few months.

A cross country move is far easier once at a senior level or if it is within the same company. Possibly easier if you have any sort of potential network connection to a job in the destination locale.

If you have only worked one place then yes of course the new firm will want to talk to someone over there. Wouldn't you?

Doesn't seem like you've thought much of this through. Take some time to really plan this all out both financially and logistically.

If there are full sheets of CDs that you did the majority of by yourself, you should absolutely show them.

Lack of Revit knowledge is a fairly easy fix.  You can learn it on the job.  Most offices I've been in have a handful of strong Revit users that do the heavy lifting and the rest of the people just move things around and draw lines on top of the model.