Ajax probably won't work because of domain restrictions.
You could have a look at blind form links, though:
http://img.en25.com/Web/McAfee/blind-form-link-generator-v2.html
This page generates a link for you, parameters are basically the form field names as set on the form.
This is a simple http request, which will post your data to the form specified.
You can use it as an iframe src, or even an img src. Data will be submitted, page won't reload.
Edit regarding Seb's complaints:
The link was provided as a helper. Please note that the generator creates a link which uses &e= for the email address field value.
I have senn this fail many times, so please use the original form field name set on the eloqua form.
If you are using Eloqua Landing pages or external pages, they will most likely be hosted on a subdomain (Eloqua) or the main domain (external page) of your organization, while all form submits go to a subdomain of eloqua.com.
This means ajax will be blocked. Hence the workaround using the "blind form link" in an iframe, for example.
This link is always the same structure. Example:
http://now.eloqua.com/e/f2.aspx?elqFormName=elq-form-name&elqSiteID=123456&emailAddress=EmailAddress&firstName=value&lastName=value&checkbox=1
You can use now.eloqua.com/e/f2.aspx for all blind form submits.
The parameter "elqFormName" specifies what form the data is being sent to.
"elqSiteID" is necessary to identify your Eloqua instance.
All following parameters refer to the HTML name given for the field on the Eloqua form.
If you send a blind form submit, all processing steps in Eloqua will be triggered, but used in an iframe or img tag for "fake ajax" will not trigger any redirection set on the form in Eloqua.