Another answer addressed the situation of three p orbitals, each on separate atoms. However, the example of $\ce{H2O}$ given in the question is a bit more complicated, since two of the orbitals are on the same atom (s and p on O). The short answer is that we cannot determine qualitatively what the orbitals look like, specifically the nonbonding one that is intermediate in energy.
If we first consider the s and p orbital independently, we have four possible combinations:
- s + A1 (where " + " means same phase) [bonding]
- s - A1 [antibonding]
- p + A1 [bonding]
- p - A1 [antibonding]
But we know that only three orbitals actually result, since three went in. SO already we have a problem that we don't know which three to use. It gets even more complicated when we realize that the s and p orbitals can both contribute to the same MO. (This is often described as "s-p mixing", though it formally is a mixing of the MOs, not the AOs.) If we don't worry about the exact value of the coefficients of each orbital and just focus on sign, we have four distinct results:
- s + p + A1 [strongly bonding]
- s - p + A1 [essentially nonbonding, since the portions of s and p that are oriented towards A1 are out of phase with each other and at least partially cancel out so there is very little overlap with A1]
- s + p - A1 [strongly antibonding] here the portions of s and p oriented towards A1 are additive to make a large lobe that is out of phase with A1
- s - p - A1 [essentially nonbonding, since the portions of s and p that are oriented towards A1 are out of phase with each other and partially cancel out as in (2)]
Of these, (1) and (3) are good representations of the known bonding and antibonding orbitals in $\ce{H2O}$ that you will find in pictures of MOs of $\ce{H2O}$, although the contribution of p to (1) is small enough that it closely resembles a simple s + A1 orbital.
The challenge is the third orbital. Determining whether it will more closely resemble (2) or (4) is not something that can be done with simple qualitative analysis. We must instead do a more quantitative analysis, which tells us that (4) is more accurate; the density on O has a small lobe pointed towards A1 that is in phase with A1 but overlaps very little and a large lobe that points away from A1 that is out of phase with A1. This quantitative analysis is covered in advance MO theory texts.