I want to perform music in class for a Shakespeare play. Can I play an English horn part with a viola?
I assume you're asking whether you can play an English horn part on aviola, because you have a viola player at your disposal and not an English horn player.
It's possible, but there are a few problems:
- The viola player will be used to reading in alto clef, not the treble clef in which the English horn part is written.
- The English horn is a transposing instrument, and all music for is it written a perfect fifth higher than it sounds. This means that, when the violist plays the English horn part, they will sound a perfect fifth higher than they should (!).
It's going to be difficult to hand a violist treble clef music written at a different pitch level. Doing this properly would require some re-writing of the English horn part so that a violist could read it and perform it at the correct pitch level.
There are multiple aspects you would need to determine to see if one instrument can replace another. I will list some in the order of importance.
Is this even necessary? Is the part actually important to the piece? A lot of pieces are written with parts that may be omitted. Even if the instrument has a solo, often cues will be written for other instruments. And, of course, you may be able to find someone who can play the correct instrument.
Sound: Do the instruments sound similar? If not, does the difference sound okay to you? This really is a personal judgment, and depends on the instrumentation of the entire piece.
Range: Do the instruments share enough of their of their range to play the piece? And, if they do, does the replacement sound okay in the entire range of the song? If not, then can it be dropped or raised an octave and sound okay? (This is usually only true if the instrument is playing solo or possibly duet.)
Transposition: How easily can the replacement instrument read the actual music in the right pitches? If both instruments play the same pitches (e.g. a C on one instrument sounds the same as a C on the other one) and they are written in the same clef, this isn't a problem at all. If not, the difficulty depends on your approach.
The failsafe solution is simply to rewrite the music. The only caveat is that, in certain situations, one may be required to use original scores only.
If this is not possible, then it depends on two things: the skill of the performer to transpose on sight, how long they have to practice, and how difficult the transposition actually is.
Articulation: Can the target instrument actually make all the variations of sounds that the original? I put this last because it is the least likely to be a problem, as most instruments can do some semblance of the same articulations, assuming the original is a single note instrument and the target instrument can fully sustain a note.
Your specific case
I will assume that you have already considered number 1, so I will first address number 2. I would argue the two instruments sound fairly similar, especially with vibrato. The viola has bit more of a richer sound, while the English horn is more piercing, but they overlap a lot. The main issue would be with instrumentation: the viola can get lost in other string instruments while the English horn tends to come out above. However, having other strings play softer and the viola play louder may overcome this limitation.
Number 3 is unlikely to be a problem, as the range of the English horn is close to and completely contained within the range of the viola, based on this chart. The viola's range is C3 to E6. The English horn's range is B3-G6, but it plays a fifth lower than written, so that's actually concert E3 to C6.
Number 4 is the big one. It's possible the music is already written in alto clef. If so, then congratulations! You can just play it all as written. When the English horn is written in alto clef, the notes are the concert pitches, which is the same as for the viola.
Otherwise, it will be written in the treble clef. If you have access to music writing software, it would be easy (if possibly time consuming) to simply copy the music into the program, and then use the transpose feature. You would need to transpose down by a perfect 5th (7 semitones), and change the clef. Then you just need access to a printer or possibly a tablet.
If that is not something you (or the performer) can easily do, however, don't fret. The transposition is a fairly easy one.1 All the player needs to do is add a line below the staff, add a sharp or take away a flat in the key signature, and treat the clef as different. If they wish to write this on the score, they can draw in the addition line, clef, and accidentals in pencil, and then use a highlighter to highlight the new line and the four lower lines, to remind them not to count the top line. Or, if they are able, they could white out or erase the top line.
And number 5: as I said, this is rarely a problem. I cannot think of any articulations that the English horn can do that the viola would not be able to mimic. (The opposite is not true, of course, due to the viola having multiple strings and harmonics and infinite sustain.) It may be more or less difficult, but it should be doable. The only restraint is the ability of the performer.
 The reason this is true is that the English horn plays a fifth lower than concert pitch. Hence a second line G is actually playing middle C. In the alto clef, middle C is the third line. So adding one line and fixing the clef and key signature fixes the issue. Many players can handle the mental change on their own, especially if they have time to practice.