Let me further break these 5 modules into 2 categories, the primary modulation and the secondary modulation. The oscillator, filter and amplifier are of primary modulation. They work directly on the sound that we will hear. The secondary modulation includes the LFO and envelope, which will modulate the primary modulation during the audio signal manipulations.
Oscillator is also known as VCO, voltage controlled oscillator. The main functino of this module is to create the sound. It creates the sound with a timbre based on the waveform selected in the synthesizer. Sine wave is normally giving a single frequency range, triangle and square waveform will have the fundamental plus the odd harmonics, while sawtooth waveform will gives fundamental plus odd and even harmonics in the timbre.
Filter, or also known as VCF (voltage controlled filter), is used to shape the spectrum of the generated sound. This would determine how the generated audio signal sound, for example to sound like a tuba or a flute. This module often under the control of an envelope or LFO. The filter can be of low pass, high pass, band pass, notch or comb filter.
"Acoustic filters" by Acoustic_filters.png: Mike.lifeguard
derivative work: ¡X Mike.lifeguard - Acoustic_filters.png. Licensed under Public domain via Wikimedia Commons.
Amplifier, or VCA (voltage controlled amplifier, shape the volume of the sound signal. It amplifies or attenuates the signal before it is passed to the external. The gain of VCA can be controlled by LFO or envelop generator too.
LFO, low frequency oscillator, is used to modulate the sound with a very low frequency signal, which is normally out of the human audible range, 0Hz - 20 Hz. Similar to oscillator of the primary modulation of a synthesizer, the signal can be of any waveform. It can create vibrato effect on the sound.
Envelope provides the envelope modulation to shape the volume of the produced note. The envelope is formed by 4 parameters, attack, decay, sustain and release. All of these parameters are in time domain, except the sustain is based on the amplitude.
"ADSR parameter". Licensed under CC BY-SA 3.0 via Wikimedia Commons.
These are the 5 important modules in a synthesizer. Thanks for your time reading this. I am still in progress to identify each of these elements and the controls and how they work in the software that I have. Hopefully, I can identify them soon. Have a great day! :)