Whether or not you own the copyright really depends on your agreement with them. You say you have no contract, but you mean you have no WRITTEN contract -- you do have at least a verbal contract, which is just as binding. Further, the emails between you may actually form a written contract. You should contact an attorney who can review these emails and give you more specific advise.
Your question is a simple question, but getting to the answer can be difficult and will require a detailed review of the facts. The decision to seek legal counsel may depend on the value of the services you provided. If the fair market value of your services was $999, then you might chalk this one up to "experience" and consider taking a deposit prior to performing future work. If the fair market value of your services is considerably more, it might justify the expense of hiring an attorney. If you decide to talk to an attorney, here are a few points you might ask about:
1. The string of emails probably creates or evidences a "contract". Do they also contain details on deliverables, scope of work, pricing, etc. Keep in mind that contracts do not have to be in writing. Verbal contracts are valid, but proof (he said/she said) is the obvious challenge there.
2. Did you create a derivative work? Depending on extent of the modifications to the logo, you might have a copyright in the derivative work. If that's the case, you can approach any ISP to take down your copyrighted work. Most ISPs will have a DMCA notice that tells you how and where to file your takedown request. But don't file a takedown request lightly, because if you're not the copyright owner, you might be liable for damages if the ISP complies with your demand only to discover you didn't have the legal right to demand takedown.
3. You said you haven't been paid for any of your work, but the copyright issue might turn on whether your work qualifies as "work for hire". A good IP attorney can walk you through that analysis.
A cease and desist letter from a reputable lawyer is a good place to start. If it comes from you individually, it doesn't show you're serious about a potential lawsuit. You might also consider a small claims action if your damages are up to $7,500 and you're suing as an individual (corporations can sue for up to $5,000 in small claims court, but only twice per year). The small claims action might be more effective than a cease and desist if your primary objective is to get paid for the work you invested. But if you want to stop them in their tracks, hire a good IP lawyer and get that letter out ASAP.
The information provided here is general in nature. This is not specific legal advice and does not create an attorney-client relationship. To obtain legal advice, consult with and hire an attorney licensed to practice law in your state.
Potentially, you could sue for breach of contract, and injunction to stop use of the logo. However, you really should take everything to an attorney for a consultation, including the logo, any emails, and the websites.
There seems to be an epidemic of situations in which large corporate entities fail to pay independent designers the amount agreed for their services and designs. In such a situation, where there is an oral agreement (perhaps substantiated by e-mails and text messages), the free lance designer may assert claims for breach of contract and/or copyright infringement (assuming the free lance designer timely registered for copyright protection). But in situations like this, companies often assert that they did not agree to pay for the designs, that the freelance artist agreed to provide the design services in order to get experience and/or improve his resume, and that in any event, the going rate for obtaining such design services is very low--perhaps a few hundred dollars. Further, the company will argue that you granted an express oral license and/or an implied license for use of your designs. Unfortunately, where there is no written agreement, and where the artist failed to timely register for copyright protection, the companies often prevail in situations such as this----the artists recognize that the costs of pursuing suit usually far exceed the likely recovery.
The lesson here is that free lance designers should not accept work unless there is a written contract that sets forth the terms and conditions, including payment obligations, ownership of IP rights, and other related issues. If you are going to continue in the free lance web design business, you need to retain counsel to help you develop a form of contract that you can use to protect yourself in situations such as this. And each time you prepare a design for a client, you would be well-served by filing for copyright protection----this can be handled on-line for a small fee (usually $35).