The classification nominal -- ordinal -- interval -- ratio (NOIR) arguably creates as many problems as it solves. This applies to graphics too.
If you look across the overlapping literatures of statistical science, the extent to which people treat NOIR seriously varies enormously: hardly at all in modern mathematical statistics or econometrics, but quite prominently in many elementary or introductory treatments in psychology (where it originated), sociology, biology, and some other disciplines. In some of the latter treatments there is an extraordinary mix of obvious points that no-one disputes and taboos about what you can and can't do, or should or shouldn't do. It's important to grasp that there is much disagreement here between and within communities of statistical people.
To give a concrete example, a variable gender with possible values male and female would presumably be declared nominal by all. But in graphics what is usually being plotted is (say) numbers of males and females or percents of males and females. Such variables are ratio scale, in that ratios make sense (4 males/2 males = 2; 40% males/20% males = 2; 0 or 0% males is a true, not an arbitrary zero). So, the raw data in say spreadsheet form may be nominal (person 42 is female, whatever), but what is plotted is in quite different form.
More generally, most modern categorical data analysis is based on devices to represent categorical data on ratio scales, such as probability or cumulative probability.
So, I suggest that the nub of the matter is not what you call the data in their raw form but what you are actually plotting. To focus on the question, area graphs usually seem to plot fractions in either absolute or relative form. Whether the fractions represent nominal or ordinal categories is no barrier to using area graphs.
In terms of references: there is a massive literature
on the relationship (or otherwise) between measurement scales and
statistics. My own favourites are as below, partly because I think
both are relatively clear and partly because you can read dissenting
Velleman, P.F. and Wilkinson, L. 1993. Nominal, ordinal, interval,
and ratio typologies are misleading. The American Statistician 47:
65-72. See also follow-up under "Letters to the Editor" in 47(4) and
[I note incidentally that the comment by David J. Hand is reported as
if from "David J. Hand and Milton Keynes". That was a mistake: "Milton
Keynes" is not a person, but a place, the town where Hand's then
institution, the Open University, is based.]
Hand, D.J. 1996. Statistics and the theory of measurement.
Journal of the Royal Statistical Society. Series A (Statistics in
Society) 159: 445-492.
(LATER) Two further specific examples may help focus discussion, especially if you disagree with them.
A presentation I saw included bar graphs of sex ratio for various Indian states and territories, the bars drawn with base zero and so to a first approximation all very similar in length. I suggested that base 1 (100%) would be a more effective choice, enabling differences between values to show up much more clearly. This was met with the dogma "But all bar graphs should start at zero because bar lengths encode values!". I see the point, but the point can often just lead to ineffective graphs. Also, bars are just being drawn to encode (value - reference value) and that scale has a zero, the reference value. It is a tough call if the audience is not expected to understand subtraction.
Similarly, bar graphs are often used to show time series (e.g. of monthly averages) in climatology to show temperatures: the bars show temperatures above or below freezing (base at freezing point) or above or below mean temperature. Almost everybody outside the US uses Celsius; in the US people often use Fahrenheit. Both these scales, temperature - freezing point, or temperature - mean, are interval scales, but I have yet to meet a purist who insists on showing bar graphs of climatic data with temperatures in Kelvin and base at 0 K.