ために

1. 1In order to or for the sake of; marks the purpose of a deliberate action.Ex. 1
2. 2Because of or due to; marks the cause of a situation or result.Ex. 2

The purpose sense is common in speech and writing, typically with volitional verbs where the subject's own action achieves the goal. The cause sense is somewhat stiffer and often appears in news, announcements and explanations of events. Compared with から or ので, the cause sense sounds more objective and formal.

• んがためN1んがため corresponds only to the purpose sense of ために: attach it to a verb's ない form minus ない (する→せん). It has a strong classical written flavor and emphasizes determination at any cost, but cannot attach to nouns or express reason.
• べくN1べく also corresponds only to the purpose sense of ために, attaching only to a verb's dictionary form (する usually becomes すべく). It does not attach to nouns, is formal and literary, and is rare in daily conversation; the reason sense of ために cannot be replaced with べく.
• ように/ようなN3ように/ような expresses metaphor, example, or 'just as...' — not purpose or reason — so it is not interchangeable with ために. When the first clause uses a potential form or a non-volitional verb, ように expressing purpose is a separate usage.
• からN5から is close to ために only in the reason sense: から is more subjective and its following clause can contain requests, commands, or volition, while ために is more objective and formal and does not introduce requests or commands. Nouns and な-adjectives take だ／です before から, but の and な before ために.
• のでN5ので expresses only reason, so it is close only to the reason sense of ために. ので can be followed by requests or suggestions, which the reason sense of ために generally cannot, and ために sounds more formal; nouns take なので vs. のために respectively.
• せいでN3せいで expresses only reason, not purpose, and is mostly used for bad results with a tone of displeasure or blame. For the reason sense, use ために for objective statements and せいで when you want to say 'it's all because of...'.

ために expresses both purpose and reason, so first determine which meaning is intended. For purpose it corresponds to べく and んがため, which attach only to verbs (not nouns) and are formal/written, with んがため emphasizing resolve at any cost; neither can express reason. For reason, から and ので can be followed by requests etc., while ために is more objective and formal and does not introduce requests or commands; せいで is mostly used for bad results with a blaming tone. ように／ような expresses metaphor or example and is not interchangeable with ために.