The thing I don't like about being tied to a PCB vendor is that you do all the work and then you end up with nothing you can carry away with you.
And if you seriously want to do controlled impedance work then you must have the freedom to choose your PCB materials, stackup and maybe even fab house.
EasyEDA supports a single set of PCB track design rules but tracks can be modified on a per track basis so you can manuall define tracks that you need to be specific widths.
For a defined impedance you will then have to specify a substrate material and - if it's really important - a material manufacturer.
You will also have to specify the layer spacings. EasyEDA currently uses a default set of layer spacings and the material is uncontrolled. You can contact EasyEDA via their support email address to discuss your requirements or to find out what the default stackup and materials are and then design the trace widths to suit.
If that isn't enough then you still have the option to specify what you want in the design in EasyEDA, generate and download the Gerbers at the end of the design _and then take them to a PCB fab house than can make exactly what you want_.
That's the crucial bit that you can't get with a tied-in free tool.
I don't think any online tool (certainly not a free one, unless the free version of Upverter supports it?) allows you to define a trace impedance and then have it work out the required trace width for you on a given substrate and stackup.
KiCad has a trace impedance calculator built into it but that is not tied into any form of Design Rule definition or checking. There are many similar online trace impedance calculators that would give adequate trace dimensional information consistent with the degree of impedance control precision you might be able to achieve using EasyEDA.
It's not unitil you get up to the higher end tools like Altium (maybe), Cadence and Mentor that you get true controlled impedance design capability. In tools like that you can specify the detailed layer stackup and then specify trace impedances in the schematic. Then they are passed through into PCB layout and actually define the trace dimensions.
All of that information is then used to run Signal Integrity simulations and, in some tools, RF and Microwave simulations.
That said, it is possible to create quite effective simulations of controlled impedance circuits in EasyEDA because the underlying ngspice engine supports a range of transmission line structures.
It's fiddly to set up and again is not tied into the PCB design rules in any way: it just shows what the circuit would do if the PCB had all the right impedances in it. You still have to manually calculate all the PCB trace width and stackup dimensions, taking into account the dielectric constant of the substrate material. That can be partially automated by building parameterised expressions into the simulation to incoporate those given substrate parameters. If you wanted to go into that much depth, I'm sure contacting support at EasyEDA would get you some further guidance on this.
:)