What is difference between homogeneous and isotropic material? When do we say a material is isotropic? When properties such as density, Young's modulus etc. are same in all directions. If these properties are direction-dependent then we can say that the material is anisotropic.
Now, when do we say a material is homogeneous? If I have steel with BCC crystal structure, when do we say that this is homogeneous and non-homogeneous? Can someone give specific examples to explain - especially what a non-homogeneous material would be?
 A: In short, to my understanding:
homogeneous : the property is not a function of position, i.e. it does not depend on $x$, $y$ or $z$.
isotropic: the property does not depend on a particular direction.
NB: you can have a homogenous property that is not isotropic, i.e. the refractive index of a birefringent material: it is a constant, but this constant has two different values along the two axes of the material.
A non-homogeneous material could be, say, the Earth itself: its density depends on whereabouts you are (which layer, crust, mantle etc.).
A: Homogeneity = translational invariance
A material is homogeneous with respect to the property $f$ (for example density) if
$$f(\mathbf r) = f (\mathbf r + \mathbf r')$$
i.e. property $f$ does not depend on the spatial position. If you measure property $f$ at point $\mathbf r$ or $\mathbf r+\mathbf r'$, you will find the same result.
Examples: most materials are homogeneous at a large enough scale, but they can reveal inhomogeneities if we look close enough. See the section about scale.
Isotropy = rotational invariance
A material is isotropic with respect to the property $f$ if
$$f(\mathbf r) = f (|\mathbf r|)$$
i.e. property $f$ does not depend on the direction of its argument. If you measure property $f$ along any direction in the material, you will find the same result.
Examples: fluids and amorphous solids are isotropic. Most crystals (with a few exceptions like the cubic crystal system) are not isotropic.
Scale dependence
Notice that both homogeneity and isotropy are scale-dependent quantities: they depend on the spatial scale where we choose to effectuate our measurements.
To give you a specific example, consider steel: steel is an iron-carbon alloy. At a large enough scale (let's say the mm scale), steel is homogeneous. However, if you look at it close enough ($\mu$m scale), this is what you see (source):

Definitely not homogeneous. Another example is granite:

Other examples of materials which are homogenous/isotropic on large scales but inhomogeneous/anisotropic on smaller scales, apart from alloys, are polycrystalline materials.
Also a normal simple cubic crystal (figure below), which is isotropic on large scales, is anisotropic on small scales. To see this, just think about standing in the center of the cube: how many atoms will you encounter if you move towards one of the faces? And how many if you move along one of the diagonals? The answer is different.

To conclude, I will just remark that homogeneity and isotropy are independent from each other. Below you can see an homogeneous but not isotropic pattern on the left and an isotropic but not homogeneous pattern on the right (source).

Edit: I should have specified this, but a material can be isotropic with respect to a point. The figure on the right is isotropic with respect to its center, however it is clearly not isotropic with respect to all points. If it was isotropic with respect to more than 1 point, it would also be homogeneous.
A: Further to your example, although a block of steel with BCC crystal structure may be considered homogeneous and isotropic, industrial processing such as heat treatment, annealing, cold rolling and welding can be used to create anisotropic stress-strain relationships. For example, if a steel rod is heated at one end, it would be considered non-homogenous, however, a structural steel section like an I-beam which would be considered a homogeneous material, would also be considered anisotropic as it's stress-strain response is different in different directions.
A: I think a body is homogeneous when the properties that defines its physical structure are same at all points(or space)
while a body is isotropic if the value of properties,that affect some physical phenomenon,is same in all directions
