There is no relation between orbitals and Bohr's orbits: orbitals
derive from the principles of quantum mechanics and have a precise
physical meaning; Bohr's orbits are just a try to put some numbers
together and have only (limited) historical meaning. You say that same
people (who?) state that orbitals are energy eigenstates (?) and shapes
are non-sense (?); well, this is objectively and undoubtedly false.

First of all, orbital are functions . The only confusion in this matter
is whether one means wave functions (the eigenfunction of the energy
operator, called Hamiltonian) or their squared absolute values; the
latter is the commonest convention. Eigenvalues are numbers, not
functions.
The squared absolute value of a wave function (|ps|2 now on; I do not
want to use Greek letters now) has a precise, measurable, physical
meaning: the density of probability of finding the system in that point
of the space; thus you can calculate the probability of finding an
electron in a certain region by integrating the |ps|2 in that region.
This is a principle of quantum mechanics, just like Newton's laws in
classical machanics or Maxwell's laws in electromagnetism.

Anyhow there is a problem when we want to rapresent this |ps|2 since it
is a function of three indipendent variables (density of probability
for every point in three dimensional space), thus a four-dimensional
graph would be necessary. Since we leave in a three dimensional world
we cannot have a totally satisfactory graph of it, but we can rapresent
it in many different ways that can give a hint of the whole function.
This problem is similar to that of rapresenting temperatures of a
region on the earth on a two-dimensional map and in some cases the same
convenctions for graphs are used.
Here's a list of the most usual ways for rapresenting orbitals
(intended as |ps|2):
- isosurfaces: surfaces formed by points sharing the same value of the
function (like isotherms on the temperature map mentioned above). Since
this surfaces tipically contain each other, only one is rapresented;
which surface is arbitrary, but the surface containing the 90% of
probability (that's to say the integral of |ps|2 inside that surface is
0.9) is often chosen. This is the commonest rapresantation.
-shaded filling. The color of a point varies as the value of the
functions (the same solution is often used in a temperature map). These
graphs are beautiful, but not very clear.
- Angular probability. The graph is a surface; the distance of a point
from the center of the coordinates is equal to the integral of |ps|2 in
that direction from the centre to infinity; this is the density of
probability of finding the electron in that particular direction, no
matter how far from the nucleus. These graphs look similar to those of
isosurfaces, but they have a different meaning.
- Radial probability. These are two-dimensional graphs that show the
value of |ps|2 in function of the distance from the nucleus, integrated
around angles. This is the probability of finding the electron on a
spherical surface of that particular radius, no matter in which
direction.

|ps|2 is density of probability but the wave function (ps now on)
contains more information than |ps|2, that we might need. In fact ps
contains the full information about the state of the system (another
principle of quantun machanics). The rappresantation of ps is more
difficult than that of |ps|2 since it is a complex function and thus
would need a five-dimension graph to show it completely. The usual
choice is to put additional information about |ps|2 graphs in two
steps:
- the set of ps corrisponding to the same value of total angular
momentum (i.e. the orbitals that have the same letter: p, d, f) are
combined to make them real. This process is possible because all these
orbitals have the same energy, and the resulting orbitals are just as
good (as long as they are indipendent and normalized); anyhow the
original orbitals are also eigenfunctions of the projection of angular
momentum (they have a definite value of m), the resulting orbitals are
not: the electron still have a definite absolute value of m, but the
sign is lost, which means that electron can spin left or spin right
around the nucleus with equal probability. The orbital with m=0 is
already real and is left unchanged; this is simmetric around z axis and
for l>1 looks different from the other orbitals.
If we plot the probability of the original orbitals, we totally lose
the information about phase and the orbitals sharing the same absolute
value of m would have exactly the same graph.
-the memory of the sign is kept by plotting |ps|2 graph in different
colors corresponding to the sign in the original ps. Sign is very
important to understand interactions of bonding atoms and for many
other properties.

So, it does make sense to speak of the shapes of orbitals, and they
deeply affect properties of atoms. Orbitals are the distribution of
electron density in the space just like clouds are the distribution of
water in the sky (and they also have a shape).

Bye