Most sources which I encountered say that English consonants [p], [t], [k] are aspirated before a vowel but not after [s], and become unaspirated after [s]. Canonical example: [p] is strongly aspirated in "pear", but unaspirated in "spear". My question is: what about the position of [p], [t], [k] before another consonant, notable before [r] or [l]? Examples: plane, pride, train, clue, crow etc. Are [p], [t], [k] in these cases aspirated or not?
When we make a voiced sound, for example a vowel sound, our vocal cords vibrate. This gives the sound pitch. We can make voiced sounds with a high pitch or a low pitch. For this reason, you can sing a tune using a [z] sound. You cannot do this, for example, with an unvoiced sound like [s]. We don't vibrate our vocal folds for an [s] sound, so it has no musical pitch. All vowel sounds are voiced, of course.
When the voiceless plosives [p, t] or [k] occur at the beginning of a stressed syllable in English, they have an effect on the following voiced sounds. In English there are rules about what types of sound can occur after these consonants when they occur at the beginning of a syllable (these are called phonotactic rules or phonotoactic constraints). English only allows the consonants /r, l, w, j/ or a vowel after a /p, t/ or /k/ at the start of a syllable.
Now, the phonemes /r, l, w, j/ and the vowel sounds are voiced. This means that they have pitch and that our vocal cords vibrate when we make them. However, after [p, t, k] at the beginning of a stressed syllable something strange happens. There is a delay before our vocal cords start vibrating. So, for example, in the word pool /pu:l/, there is a gap between our lips opening for the [p] and our vocal cords vibrating for the following [u]. This gap is called the Voice Onset Time. The Voice Onset Time in English is quite long in this situation. After we release our lips for the [p] in pool air starts rushing out of our mouths as it is pushed up from the lungs. During the gap between the [p] and our vocal folds starting to vibrate, we can hear this air rushing out of our mouths. It sounds like an [h]. In a word like pool where the sound after the plosive is a vowel sound, we call this [h]-like quality at the beginning of the vowel aspiration. Really what we are hearing is a devoiced vowel. Our mouths are already making the vowel shape but the vocal cords have not started vibrating yet.
Exactly the same thing happens when the sound after the [p, t] or [k] is one of the approximant sounds [r, l, w, j]. There is a gap after the release of the [p, t] or [k] before the vocal folds start vibrating. So in the word clean /kli:n/, for example, there is a gap after the [k] sound before the vocal folds start vibrating for the voiced [l]. During this gap our mouths are already making the necessary [l] shape but there is no vocal fold vibration. We will hear the air rushing out of the mouth from the lungs. It will have an [h]-like quality, but it will have an [l]-like quality too. In this situation we say that the [l] has become devoiced. However, we do not call the hissing noise that we hear aspiration when it occurs during a consonant sound like [r, l, w, j].
The Original Poster's question
When [p, t] or [k] occur at the beginning of a stressed syllable, they cause a delay in the voicing of the following sound. This delay is known as the voice onset time. During the delay we will hear a devoiced version of the following vowel or consonant. There will be a hissing noise as the air escapes from the lungs before the vocal cords start to vibrate. This happens regardless of whether the following sound is a vowel or a consonant such as [r, l, w, j]. When the following sound is a vowel we call this hissing noise aspiration but when the following sound is a consonant such as [r, l, w] or [j], we just say that the consonant has become devoiced.
You can hear a nice example of this type of devoicing on this page by Goeff Lindsey.
I have used the [r] symbol to represent the sound we make when we say an English /r/. This is to make the post easily readable. However, the standard English /r/ sound is technically not [r], but [ɹ].
A /p/, /t/ or /k/ is aspirated when it is the first consonant of a stressed syllable, whether it is followed by a vowel or by a semivowel or liquid consonant. The words plane, pride, train, clue, crow all start with aspirated stops.
As Araucaria's answer says, in a consonant cluster consisting of a syllable-initial voiceless stop phoneme + a consonant such as /l/, /r/, /j/ or /w/ the "aspiration" of the stop is realized largely as devoicing of the following consonant (I think it can be devoiced entirely, but perhaps more commonly it is only "partially devoiced" with a voiced second part before transitioning to the following vowel). This is not really a big difference phonetically from the situation before a vowel since aspiration before a vowel largely consists of partially devoicing the vowel.
It is of course good to remember that in English, "clusters" of consonants that fall within the same syllable tend to be very coarticulated; they are pronounced with one "breath" and not separated by any kind of pause or intermediate release. The aspirated release of the syllable-initial stop is more or less simultaneous with the pronunciation of the second consonant; you don't wait for the release before starting to pronounce the second consonant. (In fact, as TRomano and Araucaria mention in the comments below Araucaria's answer, the "second" consonant generally affects the pronunciation in subtle ways even before the release of the "first" consonant: for example in a cluster like /kj/ the /k/ will start out with a more fronted pronunciation (phonetically [k̟] or [c]) in anticipation of the phonologically later palatal glide phoneme /j/. So terms like "first" and "second" consonant make sense phonologically, but not so much phonetically.)
It's important to differentiate in this regard between consonant clusters that occur at the start of a syllable, such as pl-, kr-, tw-, and consonant clusters that occur between syllables, such as pt, kt. The syllable-initial /p/ in "apply" is almost always aspirated, but the syllable-final /p/ in "optician" almost never is. Instead, the release of the /p/ is "masked" by the transition to the following plosive /t/ (which does have an aspirated release, since it is at the start of a stressed syllable).
There is no outpuff of air between [p] and [l] or between [k] and [l], or between [p],[k], or [t] and [r].
P.S. Because there is no "between" there to speak of. The mouth is in position to produce both sounds from the outset. The mouth (tongue, cheeks, lips) is in position to produce [kr], for example. As the cheeks are relaxing to resolve the [r] and transition to the vowel, the voicing occurs.
The combinations sp, st, pl, pr, cl, cr, tr etc. are digraphs - meaning they are two letters which make a single sound - they are pronounced together, with no aspiration between.