When we can call a quark (or gluon) a struck parton? For example in a semi-inclusive inelastic scattering, a quark (inside a nucleon) can receive momentum fraction from the lepton that it interacted with. If the x value is high towards 1, the quark is most probably valence quark. Can we call it struck quark?  How different it is than an active quark?
 A: Here is a table of the quarks that we have determined experimantally:

The "flavor" is the left most column, the name that distinguishes the quark in the group representations of the theory. The quarks are distinguishable by their mass, seen in the rightmost column, a mass that they have in our present day universe after  electroweak symmetry  breakdown. That is how we found out by experiment that there are quarks, organized in group representations.

For example in a semi-inclusive inelastic scattering, a quark (inside a nucleon) can receive momentum fraction from the lepton that it interacted with. If the x value is high towards 1, the quark is most probably valence quark. Can we call it struck quark?

All jets identified in the interaction are "struck" by definition of interaction.
Here is an event full of jets from LHC

Keep in mind that the "flavor" of the jet is identified  by determining the leftmost column identification of the jet, for example there is one  strange (or top or bottom) particle  identified in the jet, so the jet can be assigned a strangeness quantum number. Particle antiparticle pairs cancel in flavor , so a total strangeness should be identified in the example.

How different it is than an active quark?

By the definition you provided, "active flavors"( a term not used extensively in the link) describes whether in the experiment under consideration, the electron  has enough energy so that  there is some probability to hit a high mass flavor like a bottom or a top and generate a real jet with that flavor.
For example in a  5 GeV electron proton scattering event the probability of hitting a charm, from a charm anticharm in the sea, and create a real jet  will be very low.
